Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
528 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 528 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. #22601352 | C2 | semidirect |
| 2. #22590603 | C2 | semidirect |
| 3. #22590601 | C2 | semidirect |
| 4. #22590401 | C2 | semidirect |
| 5. #22590395 | C2 | semidirect |
| 6. #22590374 | C2 | semidirect |
| 7. #22590248 | C2 | semidirect |
| 8. #22590203 | C2 | semidirect |
| 9. C4×D16×C71 | C2 | semidirect |
| 158. C4×D16 | D71 | semidirect |
| 159. C71 | #33970 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601352 | 2 |
| #22590603 | 2 |
| #22590601 | 2 |
| #22590401 | 2 |
| #22590395 | 2 |
| #22590374 | 2 |
| #22590248 | 2 |
| #22590203 | 2 |
| C4×D16×C71 | 2 |
| #33970 | 71 |