Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
566 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 99 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×#17989030 | C2 | semidirect |
| 2. C22×#14556535 | C2 | semidirect |
| 4. C2×#17988393 | C2 | semidirect |
| 5. #22610844 | C2 | semidirect |
| 6. #22608021 | C2 | semidirect |
| 7. C2×#361×C73 | C2 | semidirect |
| 45. C2×Dic292 | D4 | semidirect |
| 61. C2×#11924003 | D4 | semidirect |
| 76. M32×C73 | D4 | semidirect |
| 205. C2×#361 | D73 | semidirect |
| 209. C73 | #13338 | semidirect |
| 271. M32 | C22⋊D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989030 | 2 |
| C22×#14556535 | 2 |
| #22620412 | 2 |
| C2×#17988393 | 2 |
| #22610844 | 2 |
| #22608021 | 2 |
| C2×#361×C73 | 2 |
| #13338 | 73 |