Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
420 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 53. #14556047 | Q8 | semidirect |
| 67. #101×C71 | Q8 | semidirect |
| 198. C71 | #13302 | semidirect |
| 253. #101 | Dic142 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22593550 | 2 |
| #22588334 | 2 |
| #101×Dic71 | 2 |
| #22586467 | 2 |
| #22586466 | 2 |
| C71×#1394 | 2 |
| #13302 | 71 |