Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
310 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 17. #17988405 | C4 | semidirect |
| 110. Dic73 | #365 | semidirect |
| 123. C73 | #13183 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988410 | 2 |
| C2×#17988409 | 2 |
| #22611686 | 2 |
| #22610086 | 2 |
| #108×Dic73 | 2 |
| #22608031 | 2 |
| C73×#1383 | 2 |
| #13183 | 73 |