Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
512 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 2. #22618528 | C2 | semidirect |
| 3. #22611646 | C2 | semidirect |
| 4. C2×#17988389 | C2 | semidirect |
| 5. C2×#17988370 | C2 | semidirect |
| 6. #22608041 | C2 | semidirect |
| 7. C73×#1382 | C2 | semidirect |
| 14. #17988858 | C4 | semidirect |
| 39. C2×D584 | C2×C4 | semidirect |
| 68. #108×C73 | C2×C4 | semidirect |
| 195. #1382 | D73 | semidirect |
| 196. C73 | #12996 | semidirect |
| 252. #108 | C4×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988858 | 2 |
| #22618528 | 2 |
| #22611646 | 2 |
| C2×#17988389 | 2 |
| C2×#17988370 | 2 |
| #22608041 | 2 |
| C73×#1382 | 2 |
| #12996 | 73 |