Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1434 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 1434 conjugacy classes of subgroups — too many to draw. Only its 191 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C32×#127 | C2 | semidirect |
| 2. #10596276 | C2 | semidirect |
| 3. C2×#64141 | C2 | semidirect |
| 4. C2×#63660 | C2 | semidirect |
| 5. #10592914 | C2 | semidirect |
| 6. C2×#63632 | C2 | semidirect |
| 7. #10589389 | C2 | semidirect |
| 30. C2×C3×#127 | D3 | semidirect |
| 52. C2×C32×D4 | D4 | semidirect |
| 61. C2×C4⋊(C3⋊D3) | D4 | semidirect |
| 63. C2×#634 | D4 | semidirect |
| 65. C32×C42 | D4 | semidirect |
| 70. C4⋊(C3⋊Dic3) | D4 | semidirect |
| 75. #3748 | D4 | semidirect |
| 142. C2×#127 | C3⋊D3 | semidirect |
| 162. C2×C3×D4 | #67 | semidirect |
| 175. C3×C42 | #67 | semidirect |
| 300. C2×D4 | #638 | semidirect |
| 317. C42 | #638 | semidirect |
| 339. C32 | #2002 | semidirect |
| 408. C3 | #71769 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#127 | 2 |
| #10596276 | 2 |
| C2×#64141 | 2 |
| C2×#63660 | 2 |
| #10592914 | 2 |
| C2×#63632 | 2 |
| #10589389 | 2 |
| #71769 | 3 |