Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
701 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 701 conjugacy classes of subgroups — too many to draw. Only its 122 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. C22×C32×D8 | C2 | semidirect |
| 2. C2×C3×#826 | C2 | semidirect |
| 3. C3×#5115 | C2 | semidirect |
| 4. C3×#4562 | C2 | semidirect |
| 5. C3×#4549 | C2 | semidirect |
| 7. #72035 | C3 | direct (N × H) |
| 14. C2×C3×D24 | C22 | semidirect |
| 17. C3×#818 | C22 | semidirect |
| 18. C2×C3×C3⋊C16 | C22 | semidirect |
| 20. C22×C3×D8 | D3 | semidirect |
| 21. C22×C3×D8 | C2×C3 | semidirect |
| 24. C2×#826 | C2×C3 | semidirect |
| 25. #5115 | C2×C3 | semidirect |
| 28. #4562 | C2×C3 | semidirect |
| 29. #4549 | C2×C3 | semidirect |
| 40. C32×D8 | D4 | semidirect |
| 67. C2×D24 | C22×C3 | semidirect |
| 74. #818 | C22×C3 | semidirect |
| 75. C2×C3⋊C16 | C22×C3 | semidirect |
| 95. C22×D8 | C3×D3 | semidirect |
| 130. C3×D8 | #67 | semidirect |
| 131. C3×D8 | C3×D4 | semidirect |
| 154. C22×C32 | D16 | semidirect |
| 243. D8 | C3×#67 | semidirect |
| 273. C22×C3 | #826 | semidirect |
| 274. C22×C3 | C3×D16 | semidirect |
| 291. C32 | #2184 | semidirect |
| 337. C22 | C3×#826 | semidirect |
| 344. C3 | #72035 | direct (N × H) |
| 345. C3 | C3×#2184 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×D8 | 2 |
| C2×C3×#826 | 2 |
| C3×#5115 | 2 |
| C3×#4562 | 2 |
| C3×#4549 | 2 |
| C3×#2184 | 3 |
| #72035 | 3 |