Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
318 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 33. C2×#11924003 | Q8 | semidirect |
| 48. C2×C16×C73 | Q8 | semidirect |
| 52. #106×C73 | Q8 | semidirect |
| 127. C73 | #13459 | semidirect |
| 159. C2×C16 | Dic146 | semidirect |
| 168. #106 | Dic146 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620454 | 2 |
| #22611704 | 2 |
| #22611703 | 2 |
| #22610685 | 2 |
| #22608032 | 2 |
| #22608010 | 2 |
| C73×#1384 | 2 |
| #13459 | 73 |