Finite Group DatabasebetaFinite Group DatabasebetaOrder 17728.
426 conjugacy classes of subgroups; only the 194 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 194 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C277 | C23 |
| commutator, Frattini, cosocle | C22 | C24×C277 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C277 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×D4×C277 | C2 | semidirect |
| 2. C22×D4×C277 | C2 | semidirect |
| 3. C23×C4×C277 | C2 | semidirect |
| 4. #121×C277 | C2 | direct (N × H) |
| 5. C2×C4⋊C4×C277 | C2 | semidirect |
| 6. C2×C22⋊C4×C277 | C2 | semidirect |
| 11. C2×D4×C277 | C22 | semidirect |
| 12. C2×D4×C277 | C22 | semidirect |
| 17. C22×C4×C277 | C22 | semidirect |
| 18. C4⋊C4×C277 | C22 | semidirect |
| 19. C22⋊C4×C277 | C22 | semidirect |
| 25. C23×C277 | D4 | semidirect |
| 34. C2×C4×C277 | D4 | semidirect |
| 47. C22×C277 | C2×D4 | semidirect |
| 52. C4×C277 | C2×D4 | semidirect |
| 55. C2×C277 | #121 | direct (N × H) |
| 59. C277 | C2×#121 | direct (N × H) |
| 60. C2×#121 | C277 | direct (N × H) |
| 61. C22×D4 | C2×C277 | semidirect |
| 62. C22×D4 | C2×C277 | semidirect |
| 63. C23×C4 | C2×C277 | semidirect |
| 64. #121 | C2×C277 | direct (N × H) |
| 65. C2×C4⋊C4 | C2×C277 | semidirect |
| 66. C2×C22⋊C4 | C2×C277 | semidirect |
| 71. C2×D4 | C22×C277 | semidirect |
| 72. C2×D4 | C22×C277 | semidirect |
| 77. C22×C4 | C22×C277 | semidirect |
| 78. C4⋊C4 | C22×C277 | semidirect |
| 79. C22⋊C4 | C22×C277 | semidirect |
| 85. C23 | D4×C277 | semidirect |
| 94. C2×C4 | D4×C277 | semidirect |
| 107. C22 | C2×D4×C277 | semidirect |
| 112. C4 | C2×D4×C277 | semidirect |
| 115. C2 | #121×C277 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×C277 | 2 |
| C23×C4×C277 | 2 |
| #121×C277 | 2 |
| C2×C4⋊C4×C277 | 2 |
| C2×C22⋊C4×C277 | 2 |
| C2×#121 | 277 |