Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
284 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 62 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 |
|---|---|---|
| 1. #22626306 | C2 | semidirect |
| 2. #22626153 | C2 | semidirect |
| 3. #22624938 | C2 | semidirect |
| 4. #22624937 | C2 | semidirect |
| 5. #22624935 | C2 | semidirect |
| 6. #22624934 | C2 | semidirect |
| 144. C73 | #11912 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626306 | 2 |
| #22626153 | 2 |
| #22624938 | 2 |
| #22624937 | 2 |
| #22624935 | 2 |
| #22624934 | 2 |
| #22620561 | 2 |
| #11912 | 73 |