Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
330 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 78 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. #10592839 | C2 | semidirect |
| 2. C3×#5143 | C2 | semidirect |
| 4. C2×#63547 | C2 | semidirect |
| 5. #10589144 | C2 | semidirect |
| 6. #10589129 | C2 | semidirect |
| 7. #10589126 | C2 | semidirect |
| 29. #5143 | D3 | semidirect |
| 275. C32 | #2223 | semidirect |
| 312. C3 | #71093 | semidirect |
| 313. C3 | #71097 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592839 | 2 |
| C3×#5143 | 2 |
| C3×#5142 | 2 |
| C2×#63547 | 2 |
| #10589144 | 2 |
| #10589129 | 2 |
| #10589126 | 2 |
| #71097 | 3 |
| #71093 | 3 |