Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
555 conjugacy classes of subgroups; only the 182 normal subgroups are shown.
This group has 555 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. #10589672 | C2 | semidirect |
| 3. C8×Q8×C9 | C2 | semidirect |
| 5. #10588515 | C2 | semidirect |
| 7. #10588361 | C2 | semidirect |
| 69. Q8×C9 | SD16 | semidirect |
| 89. C8×Q8 | D9 | semidirect |
| 187. C9 | #3359 | semidirect |
| 192. Q8 | #3664 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D36 | 2 |
| #10589672 | 2 |
| C8×Q8×C9 | 2 |
| #10588525 | 2 |
| #10588515 | 2 |
| C4×#3664 | 2 |
| #10588361 | 2 |
| #79925 | 3 |