Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
375 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 375 conjugacy classes of subgroups — too many to draw. Only its 92 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×Q8×C9 | C2 | semidirect |
| 2. #10588773 | C2 | semidirect |
| 3. #10588710 | C2 | semidirect |
| 5. #10588224 | C2 | semidirect |
| 6. #10588212 | C2 | semidirect |
| 7. D4⋊(C9⋊C8) | C2 | semidirect |
| 83. Q8×C9 | D8 | semidirect |
| 85. D4×C9 | SD16 | semidirect |
| 104. D4×Q8 | D9 | semidirect |
| 244. C9 | #1627 | semidirect |
| 251. Q8 | #3673 | semidirect |
| 258. D4 | #3675 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Q8×C9 | 2 |
| #10588773 | 2 |
| #10588710 | 2 |
| #10588698 | 2 |
| #10588224 | 2 |
| #10588212 | 2 |
| D4⋊(C9⋊C8) | 2 |
| #71914 | 3 |