Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
514 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 514 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 |
|---|---|---|
| 1. #22596978 | C2 | semidirect |
| 2. #22586783 | C2 | semidirect |
| 3. #22586674 | C2 | semidirect |
| 4. #22586204 | C2 | semidirect |
| 32. C4×C71⋊C8 | D4 | semidirect |
| 188. C71 | #9494 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22596978 | 2 |
| #22586783 | 2 |
| #22586674 | 2 |
| #22586204 | 2 |
| C71×#2598 | 2 |
| #9494 | 71 |