Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
522 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22626936 | C2 | semidirect |
| 3. #22626934 | C2 | semidirect |
| 37. #14556550 | C8 | semidirect |
| 39. #14556548 | C8 | semidirect |
| 40. #14556548 | C8 | semidirect |
| 46. #117×C73 | C8 | semidirect |
| 169. C73 | #8731 | semidirect |
| 191. #117 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627043 | 2 |
| #22626936 | 2 |
| #22626934 | 2 |
| #117×#64408 | 2 |
| #8731 | 73 |