Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
306 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 10. #17988989 | C4 | semidirect |
| 11. #17988985 | C4 | semidirect |
| 49. M32×C73 | Q8 | semidirect |
| 51. C2×C16×C73 | Q8 | semidirect |
| 131. C73 | #13291 | semidirect |
| 162. M32 | Dic146 | semidirect |
| 164. C2×C16 | Dic146 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620462 | 2 |
| #22610055 | 2 |
| #22608046 | 2 |
| #22608037 | 2 |
| #22608033 | 2 |
| #22608030 | 2 |
| C73×#2110 | 2 |
| #13291 | 73 |