Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
588 conjugacy classes of subgroups; only the 182 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 182 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. Q8×Dic18 | C2 | semidirect |
| 3. C8×Q8×C9 | C2 | semidirect |
| 4. #10588526 | C2 | semidirect |
| 5. #10588512 | C2 | semidirect |
| 6. #10588376 | C2 | semidirect |
| 7. C4×#3664 | C2 | semidirect |
| 69. Q8×C9 | SD16 | semidirect |
| 83. Dic18 | #41 | semidirect |
| 91. C8×Q8 | D9 | semidirect |
| 191. C9 | #3362 | semidirect |
| 196. Q8 | #3664 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589679 | 2 |
| Q8×Dic18 | 2 |
| C8×Q8×C9 | 2 |
| #10588526 | 2 |
| #10588512 | 2 |
| #10588376 | 2 |
| C4×#3664 | 2 |
| #79932 | 3 |