Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
514 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22618567 | C2 | semidirect |
| 3. #22608375 | C2 | semidirect |
| 4. #22608373 | C2 | semidirect |
| 5. #22608263 | C2 | semidirect |
| 6. #22607795 | C2 | semidirect |
| 7. C73×#1288 | C2 | semidirect |
| 62. C4×#10596831 | D4 | semidirect |
| 71. C4×C8×C73 | D4 | semidirect |
| 227. #1288 | D73 | semidirect |
| 228. C73 | #9494 | semidirect |
| 290. C4×C8 | D292 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618567 | 2 |
| #22615499 | 2 |
| #22608375 | 2 |
| #22608373 | 2 |
| #22608263 | 2 |
| #22607795 | 2 |
| C73×#1288 | 2 |
| #9494 | 73 |