Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
498 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 124 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 |
|---|---|---|
| 3. #22625147 | C2 | semidirect |
| 4. #22625125 | C2 | semidirect |
| 5. #22624763 | C2 | semidirect |
| 6. #22624762 | C2 | semidirect |
| 175. C73 | #8186 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556678 | 2 |
| #22625223 | 2 |
| #22625147 | 2 |
| #22625125 | 2 |
| #22624763 | 2 |
| #22624762 | 2 |
| #22608310 | 2 |
| #8186 | 73 |