Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1284 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 1284 conjugacy classes of subgroups — too many to draw. Only its 232 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. #22626520 | C2 | semidirect |
| 2. #22625211 | C2 | semidirect |
| 3. #22625186 | C2 | semidirect |
| 4. #22625166 | C2 | semidirect |
| 103. C23×C73 | #131 | semidirect |
| 169. C73 | #17414 | semidirect |
| 272. C23 | #14556679 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626520 | 2 |
| #22625211 | 2 |
| #22625186 | 2 |
| #22625166 | 2 |
| C2×#17989248 | 2 |
| #17414 | 73 |