Finite Group DatabasebetaFinite Group DatabasebetaOrder 13504.
334 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 162 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C211 | C24 |
| commutator, Frattini, cosocle | C22 | C24×C211 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C211 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#41×C211 | C2 | semidirect |
| 2. C22×D4×C211 | C2 | semidirect |
| 3. #127×C211 | C2 | semidirect |
| 4. #124×C211 | C2 | semidirect |
| 5. #121×C211 | C2 | semidirect |
| 6. #120×C211 | C2 | semidirect |
| 7. #117×C211 | C2 | semidirect |
| 10. C2×Q8×C211 | C22 | semidirect |
| 15. C2×D4×C211 | C22 | semidirect |
| 16. C2×D4×C211 | C22 | semidirect |
| 18. C22×C4×C211 | C22 | semidirect |
| 19. C4⋊C4×C211 | C22 | semidirect |
| 21. C22⋊C4×C211 | C22 | semidirect |
| 22. C42×C211 | C22 | semidirect |
| 35. C2×C4×C211 | D4 | semidirect |
| 57. C211 | #535 | direct (N × H) |
| 58. #535 | C211 | direct (N × H) |
| 59. C2×#41 | C2×C211 | semidirect |
| 60. C22×D4 | C2×C211 | semidirect |
| 61. #127 | C2×C211 | semidirect |
| 62. #124 | C2×C211 | semidirect |
| 63. #121 | C2×C211 | semidirect |
| 64. #120 | C2×C211 | semidirect |
| 65. #117 | C2×C211 | semidirect |
| 68. C2×Q8 | C22×C211 | semidirect |
| 73. C2×D4 | C22×C211 | semidirect |
| 74. C2×D4 | C22×C211 | semidirect |
| 76. C22×C4 | C22×C211 | semidirect |
| 77. C4⋊C4 | C22×C211 | semidirect |
| 79. C22⋊C4 | C22×C211 | semidirect |
| 80. C42 | C22×C211 | semidirect |
| 93. C2×C4 | D4×C211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#41×C211 | 2 |
| C22×D4×C211 | 2 |
| #127×C211 | 2 |
| #124×C211 | 2 |
| #121×C211 | 2 |
| #120×C211 | 2 |
| #117×C211 | 2 |
| #535 | 211 |