Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
318 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 23. #17988335 | C4 | semidirect |
| 24. #17988335 | C4 | semidirect |
| 25. #17988333 | C4 | semidirect |
| 26. #332×C73 | C4 | semidirect |
| 160. C73 | #9591 | semidirect |
| 175. #332 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626107 | 2 |
| #22626045 | 2 |
| #22625280 | 2 |
| #22625143 | 2 |
| #22624828 | 2 |
| #22624765 | 2 |
| #22608587 | 2 |
| #9591 | 73 |