Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
428 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 82 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. #22625813 | C2 | semidirect |
| 3. #22625019 | C2 | semidirect |
| 10. C2×#14556597 | C4 | semidirect |
| 15. #17988611 | C4 | semidirect |
| 16. #17988553 | C4 | semidirect |
| 18. C2×C4×C8×C73 | C4 | semidirect |
| 145. C73 | #12807 | semidirect |
| 156. C2×C4×C8 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626204 | 2 |
| #22625813 | 2 |
| #22625019 | 2 |
| #22618644 | 2 |
| #12807 | 73 |