Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
717 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 717 conjugacy classes of subgroups — too many to draw. Only its 104 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. C2×C9×#127 | C2 | semidirect |
| 2. #10589907 | C2 | semidirect |
| 3. C2×#63495 | C2 | semidirect |
| 4. #10588896 | C2 | semidirect |
| 5. C2×#63391 | C2 | semidirect |
| 6. C2×#63364 | C2 | semidirect |
| 7. #10588201 | C2 | semidirect |
| 52. C2×D4×C9 | D4 | semidirect |
| 61. C2×D36 | D4 | semidirect |
| 63. C2×Dic18 | D4 | semidirect |
| 65. C42×C9 | D4 | semidirect |
| 70. C4⋊Dic9 | D4 | semidirect |
| 75. #3667 | D4 | semidirect |
| 142. C2×#127 | D9 | semidirect |
| 300. C2×D4 | #611 | semidirect |
| 317. C42 | #611 | semidirect |
| 339. C9 | #2002 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×#127 | 2 |
| #10589907 | 2 |
| C2×#63495 | 2 |
| #10588896 | 2 |
| C2×#63391 | 2 |
| C2×#63364 | 2 |
| #10588201 | 2 |
| #71769 | 3 |