Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
717 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 717 conjugacy classes of subgroups — too many to draw. Only its 100 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. #10589932 | C2 | semidirect |
| 2. C2×#63512 | C2 | semidirect |
| 3. C2×#63436 | C2 | semidirect |
| 4. C2×C9×#104 | C2 | semidirect |
| 5. #10588813 | C2 | semidirect |
| 6. C2×#63383 | C2 | semidirect |
| 7. #10588201 | C2 | semidirect |
| 43. C2×Q8×C9 | D4 | semidirect |
| 45. C2×D4×C9 | D4 | semidirect |
| 63. C2×D36 | D4 | semidirect |
| 68. C42×C9 | D4 | semidirect |
| 73. C4⋊Dic9 | D4 | semidirect |
| 76. #3667 | D4 | semidirect |
| 143. C2×#104 | D9 | semidirect |
| 283. C2×Q8 | D36 | semidirect |
| 300. C2×D4 | D36 | semidirect |
| 317. C42 | #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 |
|---|---|
| #10589932 | 2 |
| C2×#63512 | 2 |
| C2×#63436 | 2 |
| C2×C9×#104 | 2 |
| #10588813 | 2 |
| C2×#63383 | 2 |
| #10588201 | 2 |
| #70385 | 3 |