Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
444 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 47. Q8×Dic73 | C8 | semidirect |
| 49. C4×Dic146 | C8 | semidirect |
| 51. #14556556 | C8 | semidirect |
| 56. C4×Q8×C73 | C8 | semidirect |
| 192. C73 | #7577 | semidirect |
| 218. C4×Q8 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627073 | 2 |
| C4×C4⋊#10596842 | 2 |
| #22626932 | 2 |
| #22626931 | 2 |
| #22626390 | 2 |
| #7577 | 73 |