Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
408 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 119 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. C2×#17988410 | C2 | semidirect |
| 2. C2×#17988403 | C2 | semidirect |
| 4. C2×#17988364 | C2 | semidirect |
| 6. #22610803 | C2 | semidirect |
| 24. C2×Q32×C73 | C4 | semidirect |
| 25. C2×SD32×C73 | C4 | semidirect |
| 172. C73 | #13250 | semidirect |
| 177. C2×Q32 | Dic73 | semidirect |
| 178. C2×SD32 | Dic73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988410 | 2 |
| C2×#17988403 | 2 |
| C2×#17988397 | 2 |
| C2×#17988364 | 2 |
| #22610825 | 2 |
| #22610803 | 2 |
| C2×#510×C73 | 2 |
| #13250 | 73 |