Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
472 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 147 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. #22601207 | C2 | semidirect |
| 2. #22590624 | C2 | semidirect |
| 3. #22590619 | C2 | semidirect |
| 4. #22590497 | C2 | semidirect |
| 5. #22590495 | C2 | semidirect |
| 6. #22590475 | C2 | semidirect |
| 7. #22590248 | C2 | semidirect |
| 58. D16×C71 | Q8 | semidirect |
| 140. C71 | #33956 | semidirect |
| 178. D16 | Dic142 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601207 | 2 |
| #22590624 | 2 |
| #22590619 | 2 |
| #22590497 | 2 |
| #22590495 | 2 |
| #22590475 | 2 |
| #22590248 | 2 |
| #22590216 | 2 |
| C4×D16×C71 | 2 |
| #33956 | 71 |