Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
540 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 149 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. #10592537 | C2 | semidirect |
| 3. C32×#335 | C2 | semidirect |
| 4. #10589349 | C2 | semidirect |
| 5. C8×C3⋊(C3⋊C8) | C2 | semidirect |
| 19. C3×#335 | D3 | semidirect |
| 57. C32×C8 | M16 | semidirect |
| 60. C3⋊(C3⋊C8) | D8 | semidirect |
| 63. #335 | C3⋊D3 | semidirect |
| 110. C3×C8 | ΓL(1,𝔽25) | semidirect |
| 141. C32 | #1589 | semidirect |
| 156. C8 | #3743 | semidirect |
| 171. C3 | #68563 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592537 | 2 |
| C4×#3745 | 2 |
| C32×#335 | 2 |
| #10589349 | 2 |
| C8×C3⋊(C3⋊C8) | 2 |
| #68563 | 3 |