Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
238 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 39 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 |
|---|---|---|
| 7. C22×Q16×C71 | C4 | semidirect |
| 10. #341×C71 | C4 | semidirect |
| 99. C71 | #7399 | semidirect |
| 101. C22×Q16 | Dic71 | semidirect |
| 106. #341 | Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22586461 | 2 |
| #22586278 | 2 |
| C71×#2020 | 2 |
| #7399 | 71 |