Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
555 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 555 conjugacy classes of subgroups — too many to draw. Only its 130 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×#492 | C2 | semidirect |
| 2. C3×#5088 | C2 | semidirect |
| 3. C3×#5073 | C2 | semidirect |
| 4. C3×#4695 | C2 | semidirect |
| 5. C3×#4455 | C2 | semidirect |
| 7. #71262 | C3 | direct (N × H) |
| 20. C3×#492 | D3 | semidirect |
| 21. C3×#492 | C2×C3 | semidirect |
| 23. #5088 | C2×C3 | semidirect |
| 24. #5073 | C2×C3 | semidirect |
| 25. #4695 | C2×C3 | semidirect |
| 27. #4455 | C2×C3 | semidirect |
| 75. C32×C8 | D8 | semidirect |
| 79. #492 | C3×D3 | semidirect |
| 164. C3×C8 | #213 | semidirect |
| 165. C3×C8 | C3×D8 | semidirect |
| 208. C32 | #1721 | semidirect |
| 221. C8 | C3×#213 | semidirect |
| 243. C3 | #71262 | direct (N × H) |
| 244. C3 | C3×#1721 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#492 | 2 |
| C3×#5088 | 2 |
| C3×#5073 | 2 |
| C3×#4695 | 2 |
| C3×#4455 | 2 |
| C3×#1721 | 3 |
| #71262 | 3 |