Finite Group DatabasebetaFinite Group DatabasebetaOrder 28544.
712 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 184 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×C223 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C223 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C223 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#120×C223 | C2 | semidirect |
| 2. #397×C223 | C2 | semidirect |
| 3. #394×C223 | C2 | semidirect |
| 4. #392×C223 | C2 | semidirect |
| 5. #379×C223 | C2 | semidirect |
| 8. C22×D4×C223 | C22 | semidirect |
| 10. C2×C4⋊C4×C223 | C22 | semidirect |
| 14. C2×C22⋊C4×C223 | C22 | semidirect |
| 15. #95×C223 | C22 | semidirect |
| 16. #95×C223 | C22 | semidirect |
| 19. C24×C223 | D4 | semidirect |
| 74. C223 | #2812 | direct (N × H) |
| 75. #2812 | C223 | direct (N × H) |
| 76. C2×#120 | C2×C223 | semidirect |
| 77. #397 | C2×C223 | semidirect |
| 78. #394 | C2×C223 | semidirect |
| 79. #392 | C2×C223 | semidirect |
| 80. #379 | C2×C223 | semidirect |
| 83. C22×D4 | C22×C223 | semidirect |
| 85. C2×C4⋊C4 | C22×C223 | semidirect |
| 89. C2×C22⋊C4 | C22×C223 | semidirect |
| 90. #95 | C22×C223 | semidirect |
| 91. #95 | C22×C223 | semidirect |
| 94. C24 | D4×C223 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#120×C223 | 2 |
| #397×C223 | 2 |
| #394×C223 | 2 |
| #392×C223 | 2 |
| #379×C223 | 2 |
| #2812 | 223 |