Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1170 conjugacy classes of subgroups; only the 390 normal subgroups are shown.
This group has 1170 conjugacy classes of subgroups — too many to draw. Only its 390 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 |
|---|---|---|
| 2. C2×C9×#95 | C2 | semidirect |
| 3. C4×#3676 | C2 | semidirect |
| 4. #10588346 | C2 | semidirect |
| 5. D9×#95 | C2 | semidirect |
| 6. #10588329 | C2 | semidirect |
| 7. #10588328 | C2 | semidirect |
| 13. C4×#611 | C4 | semidirect |
| 32. C22×C4×C9 | C2×C4 | semidirect |
| 40. C2×C4×D9 | C2×C4 | semidirect |
| 41. #3676 | C2×C4 | semidirect |
| 42. (C2×D9)⋊C4 | C2×C4 | semidirect |
| 43. Dic9⋊C4 | C2×C4 | semidirect |
| 45. C4×Dic9 | C2×C4 | semidirect |
| 72. #611 | C42 | semidirect |
| 86. C2×#95 | D9 | semidirect |
| 165. C22×C4 | C4×D9 | semidirect |
| 187. C9 | #2275 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#611 | 2 |
| C2×C9×#95 | 2 |
| C4×#3676 | 2 |
| #10588346 | 2 |
| D9×#95 | 2 |
| #10588329 | 2 |
| #10588328 | 2 |
| #73322 | 3 |