Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
406 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 406 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 |
|---|---|---|
| 45. Q8×Dic73 | C8 | semidirect |
| 47. C4×Dic146 | C8 | semidirect |
| 49. #14556556 | C8 | semidirect |
| 54. C4×Q8×C73 | C8 | semidirect |
| 187. C73 | #7596 | semidirect |
| 213. C4×Q8 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627074 | 2 |
| #22627073 | 2 |
| #22626932 | 2 |
| #22626931 | 2 |
| #22626390 | 2 |
| #7596 | 73 |