Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
717 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 717 conjugacy classes of subgroups — too many to draw. Only its 104 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. C9×#535 | C2 | semidirect |
| 2. C2×#63512 | C2 | semidirect |
| 3. C2×#63502 | C2 | semidirect |
| 4. C2×#63396 | C2 | semidirect |
| 5. C2×#63391 | C2 | semidirect |
| 6. #10588682 | C2 | semidirect |
| 7. #10588208 | C2 | semidirect |
| 43. C2×Q8×C9 | D4 | semidirect |
| 52. C2×D4×C9 | D4 | semidirect |
| 63. C2×D36 | D4 | semidirect |
| 64. C9×C4⋊C4 | D4 | semidirect |
| 71. C4×Dic9 | D4 | semidirect |
| 75. #3667 | D4 | semidirect |
| 141. #535 | D9 | semidirect |
| 283. C2×Q8 | #611 | semidirect |
| 300. C2×D4 | #611 | semidirect |
| 312. C4⋊C4 | #611 | semidirect |
| 339. C9 | #2002 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#535 | 2 |
| C2×#63512 | 2 |
| C2×#63502 | 2 |
| C2×#63396 | 2 |
| C2×#63391 | 2 |
| #10588682 | 2 |
| #10588208 | 2 |
| #71856 | 3 |