Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
678 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 678 conjugacy classes of subgroups — too many to draw. Only its 137 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. C32×#575 | C2 | semidirect |
| 2. #10592892 | C2 | semidirect |
| 3. #10592834 | C2 | semidirect |
| 4. #10589432 | C2 | semidirect |
| 5. #10589419 | C2 | semidirect |
| 14. C2×#3745 | C22 | semidirect |
| 18. #63644 | C22 | semidirect |
| 19. #63639 | C22 | semidirect |
| 20. C3×#575 | D3 | semidirect |
| 37. C32×Q16 | D4 | semidirect |
| 41. C32×D8 | D4 | semidirect |
| 85. #575 | C3⋊D3 | semidirect |
| 102. C3×Q16 | #67 | semidirect |
| 106. C3×D8 | #67 | semidirect |
| 179. Q16 | #638 | semidirect |
| 184. D8 | #638 | semidirect |
| 204. C32 | #2190 | semidirect |
| 245. C3 | #72112 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#575 | 2 |
| #10592892 | 2 |
| #10592834 | 2 |
| #10589432 | 2 |
| #10589419 | 2 |
| #72112 | 3 |