Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
471 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 471 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 |
|---|---|---|
| 2. #10588691 | C2 | semidirect |
| 3. #10588526 | C2 | semidirect |
| 4. #10588375 | C2 | semidirect |
| 5. C9×D4⋊C8 | C2 | semidirect |
| 6. #10588163 | C2 | semidirect |
| 7. #10588136 | C2 | semidirect |
| 18. #63431 | C22 | semidirect |
| 19. C9×C4⋊C8 | C22 | semidirect |
| 20. C4×C8×C9 | C22 | semidirect |
| 25. C4⋊(C9⋊C8) | C22 | semidirect |
| 85. D4×C9 | SD16 | semidirect |
| 102. D36 | SD16 | semidirect |
| 115. D4⋊C8 | D9 | semidirect |
| 175. C4⋊C8 | C2×D9 | semidirect |
| 178. C4×C8 | C2×D9 | semidirect |
| 262. C9 | #1629 | semidirect |
| 280. D4 | #3664 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D36 | 2 |
| #10588691 | 2 |
| #10588526 | 2 |
| #10588375 | 2 |
| C9×D4⋊C8 | 2 |
| #10588163 | 2 |
| #10588136 | 2 |
| #68195 | 3 |