Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
392 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 3. #22625499 | C2 | semidirect |
| 4. #22625489 | C2 | semidirect |
| 5. #22624828 | C2 | semidirect |
| 6. #22624766 | C2 | semidirect |
| 25. Q8⋊#10596831 | C4 | semidirect |
| 26. #17988316 | C4 | semidirect |
| 27. #17988314 | C4 | semidirect |
| 28. Q8⋊C8×C73 | C4 | semidirect |
| 188. C73 | #8903 | semidirect |
| 207. Q8⋊C8 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626631 | 2 |
| #22625804 | 2 |
| #22625499 | 2 |
| #22625489 | 2 |
| #22624828 | 2 |
| #22624766 | 2 |
| #22608312 | 2 |
| #8903 | 73 |