Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
360 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22590152 | C2 | semidirect |
| 2. #22586643 | C2 | semidirect |
| 3. #22586316 | C2 | semidirect |
| 4. #22586313 | C2 | semidirect |
| 7. #17985820 | C22 | semidirect |
| 11. #17985720 | C22 | semidirect |
| 12. C8×C71⋊C8 | C22 | semidirect |
| 63. Q16×C71 | M16 | semidirect |
| 67. D8×C71 | M16 | semidirect |
| 130. C71 | #11669 | semidirect |
| 184. Q16 | #11765849 | semidirect |
| 188. D8 | #11765849 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590152 | 2 |
| #22586643 | 2 |
| #22586316 | 2 |
| #22586313 | 2 |
| C71×#2956 | 2 |
| #11669 | 71 |