Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
662 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 662 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. C22×#14556536 | C2 | semidirect |
| 2. C22×#14556535 | C2 | semidirect |
| 4. C2×#17988387 | C2 | semidirect |
| 5. #22610790 | C2 | semidirect |
| 6. #22608008 | C2 | semidirect |
| 7. C2×#357×C73 | C2 | semidirect |
| 37. C2×Dic292 | D4 | semidirect |
| 55. C2×#11924003 | D4 | semidirect |
| 71. C2×C16×C73 | D4 | semidirect |
| 158. C2×Dic73 | SD32 | semidirect |
| 206. C2×#357 | D73 | semidirect |
| 209. C73 | #13328 | semidirect |
| 269. C2×C16 | C22⋊D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556536 | 2 |
| C22×#14556535 | 2 |
| C2×#17988962 | 2 |
| C2×#17988387 | 2 |
| #22610790 | 2 |
| #22608008 | 2 |
| C2×#357×C73 | 2 |
| #13328 | 73 |