Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
476 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 151 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. #22601205 | C2 | semidirect |
| 2. #22590617 | C2 | semidirect |
| 3. #22590615 | C2 | semidirect |
| 4. #22590495 | C2 | semidirect |
| 5. #22590487 | C2 | semidirect |
| 6. C16×Dic142 | C2 | semidirect |
| 45. D16×C71 | Q8 | semidirect |
| 118. C71 | #33947 | semidirect |
| 147. D16 | Dic142 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601205 | 2 |
| #22590617 | 2 |
| #22590615 | 2 |
| #22590495 | 2 |
| #22590487 | 2 |
| C16×Dic142 | 2 |
| D16×Dic71 | 2 |
| C4×D16×C71 | 2 |
| #33947 | 71 |