Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
408 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 1. C4×#14556661 | C2 | semidirect |
| 2. #22625486 | C2 | semidirect |
| 4. #22624817 | C2 | semidirect |
| 104. D4×C73 | #108 | semidirect |
| 125. Dic146 | #108 | semidirect |
| 163. C73 | #8670 | semidirect |
| 265. D4 | #14556661 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556661 | 2 |
| #22625486 | 2 |
| #22625267 | 2 |
| #22624817 | 2 |
| C8×#11924027 | 2 |
| #8670 | 73 |