Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
470 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 109 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. #22623033 | C2 | semidirect |
| 3. #22611668 | C2 | semidirect |
| 4. #22611666 | C2 | semidirect |
| 5. #22609974 | C2 | semidirect |
| 6. #22608038 | C2 | semidirect |
| 7. C73×#1386 | C2 | semidirect |
| 15. #17988846 | C4 | semidirect |
| 16. #17988841 | C4 | semidirect |
| 50. #14556531 | D4 | semidirect |
| 63. M32×C73 | D4 | semidirect |
| 188. #1386 | D73 | semidirect |
| 189. C73 | #13077 | semidirect |
| 238. M32 | D292 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22623033 | 2 |
| #22619594 | 2 |
| #22611668 | 2 |
| #22611666 | 2 |
| #22609974 | 2 |
| #22608038 | 2 |
| C73×#1386 | 2 |
| #13077 | 73 |