Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
436 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 15. C22×Q16×C71 | C4 | semidirect |
| 22. #427×C71 | C4 | semidirect |
| 23. #419×C71 | C4 | semidirect |
| 166. C71 | #13230 | semidirect |
| 167. C22×Q16 | Dic71 | semidirect |
| 175. #427 | Dic71 | semidirect |
| 176. #419 | Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590015 | 2 |
| #22589994 | 2 |
| #22588386 | 2 |
| #22588140 | 2 |
| C71×#3059 | 2 |
| #13230 | 71 |