Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
520 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 99 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. C22×Dic568 | C2 | semidirect |
| 4. C2×#17985814 | C2 | semidirect |
| 5. #22590059 | C2 | semidirect |
| 7. C71×#1382 | C2 | semidirect |
| 195. #1382 | D71 | semidirect |
| 196. C71 | #13322 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic568 | 2 |
| C2×#17986275 | 2 |
| #22597996 | 2 |
| C2×#17985814 | 2 |
| #22590059 | 2 |
| C2×#17985782 | 2 |
| C71×#1382 | 2 |
| #13322 | 71 |