Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
365 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 365 conjugacy classes of subgroups — too many to draw. Only its 74 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. C3⋊D3×#107 | C2 | semidirect |
| 3. C3×#4491 | C2 | semidirect |
| 4. C3×#4489 | C2 | semidirect |
| 5. #10589139 | C2 | semidirect |
| 6. #10589115 | C2 | semidirect |
| 7. #10589108 | C2 | semidirect |
| 33. #4491 | D3 | semidirect |
| 35. #4489 | D3 | semidirect |
| 271. C32 | #2232 | semidirect |
| 316. C3 | #69199 | semidirect |
| 317. C3 | #69330 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3⋊D3×#107 | 2 |
| #10590844 | 2 |
| C3×#4491 | 2 |
| C3×#4489 | 2 |
| #10589139 | 2 |
| #10589115 | 2 |
| #10589108 | 2 |
| #69330 | 3 |
| #69199 | 3 |