Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
334 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 12. #17986026 | C4 | semidirect |
| 13. #17986026 | C4 | semidirect |
| 18. C4×#11765849 | C4 | semidirect |
| 19. C2×#14556039 | C4 | semidirect |
| 174. C71 | #12865 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22596991 | 2 |
| #22588444 | 2 |
| #22586470 | 2 |
| #22586468 | 2 |
| #22586462 | 2 |
| #22586460 | 2 |
| C71×#1827 | 2 |
| #12865 | 71 |