Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
488 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 131 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. #22600744 | C2 | semidirect |
| 2. #22590619 | C2 | semidirect |
| 3. #22590529 | C2 | semidirect |
| 4. #22590519 | C2 | semidirect |
| 5. #22590497 | C2 | semidirect |
| 6. #22590440 | C2 | semidirect |
| 7. #22590173 | C2 | semidirect |
| 8. #22590125 | C2 | semidirect |
| 9. C4×D16×C71 | C2 | semidirect |
| 145. C4×D16 | D71 | semidirect |
| 148. C71 | #33922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22600744 | 2 |
| #22590619 | 2 |
| #22590529 | 2 |
| #22590519 | 2 |
| #22590497 | 2 |
| #22590440 | 2 |
| #22590173 | 2 |
| #22590125 | 2 |
| C4×D16×C71 | 2 |
| #33922 | 71 |