Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
382 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 382 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 |
|---|---|---|
| 108. C42×C71 | Q16 | semidirect |
| 180. C71 | #10523 | semidirect |
| 281. C42 | #11765855 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599682 | 2 |
| #22589317 | 2 |
| #22588457 | 2 |
| #22587031 | 2 |
| #22587030 | 2 |
| #22586214 | 2 |
| C71×#1994 | 2 |
| #10523 | 71 |