Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
602 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 602 conjugacy classes of subgroups — too many to draw. Only its 105 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. #22618971 | C2 | semidirect |
| 3. #22609920 | C2 | semidirect |
| 4. #22608357 | C2 | semidirect |
| 5. #22608355 | C2 | semidirect |
| 6. #22607789 | C2 | semidirect |
| 7. C73×#1286 | C2 | semidirect |
| 56. C4×#10596831 | D4 | semidirect |
| 65. C4×C8×C73 | D4 | semidirect |
| 216. #1286 | D73 | semidirect |
| 217. C73 | #9489 | semidirect |
| 274. C4×C8 | D292 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618971 | 2 |
| #22614833 | 2 |
| #22609920 | 2 |
| #22608357 | 2 |
| #22608355 | 2 |
| #22607789 | 2 |
| C73×#1286 | 2 |
| #9489 | 73 |