Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
375 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 375 conjugacy classes of subgroups — too many to draw. Only its 80 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. D4×Dic18 | C2 | semidirect |
| 3. #10588752 | C2 | semidirect |
| 4. #10588750 | C2 | semidirect |
| 5. D4⋊(C9⋊C8) | C2 | semidirect |
| 6. #10588161 | C2 | semidirect |
| 7. #10588160 | C2 | semidirect |
| 85. D4×C9 | SD16 | semidirect |
| 100. Dic18 | D8 | semidirect |
| 244. C9 | #1627 | semidirect |
| 258. D4 | #3672 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic18 | 2 |
| C9×#459 | 2 |
| #10588752 | 2 |
| #10588750 | 2 |
| D4⋊(C9⋊C8) | 2 |
| #10588161 | 2 |
| #10588160 | 2 |
| #71014 | 3 |