Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
514 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 97 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. #22626931 | C2 | semidirect |
| 31. #14556550 | C8 | semidirect |
| 32. #14556549 | C8 | semidirect |
| 38. #117×C73 | C8 | semidirect |
| 146. C73 | #7598 | semidirect |
| 165. #117 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627071 | 2 |
| #22626931 | 2 |
| #22626391 | 2 |
| #7598 | 73 |