Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
392 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 100 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. #10592719 | C2 | semidirect |
| 3. C3×Q8×C3⋊C8 | C2 | semidirect |
| 5. #10589097 | C2 | semidirect |
| 6. #10589094 | C2 | semidirect |
| 29. Q8×C3⋊C8 | D3 | semidirect |
| 97. C32×Q8 | SD16 | semidirect |
| 115. C3×C3⋊C8 | SD16 | semidirect |
| 203. C3×Q8 | #204 | semidirect |
| 204. C3×Q8 | #214 | semidirect |
| 249. C3⋊C8 | #215 | semidirect |
| 306. C32 | #1666 | semidirect |
| 311. Q8 | #3716 | semidirect |
| 352. C3 | #70938 | semidirect |
| 353. C3 | #71020 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592719 | 2 |
| C3×#5027 | 2 |
| C3×Q8×C3⋊C8 | 2 |
| #10590369 | 2 |
| #10589097 | 2 |
| #10589094 | 2 |
| #10589090 | 2 |
| #71020 | 3 |
| #70938 | 3 |