Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
374 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22610706 | C2 | semidirect |
| 2. #22608703 | C2 | semidirect |
| 3. #22608683 | C2 | semidirect |
| 6. #22607805 | C2 | semidirect |
| 165. C73 | #10607 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22610706 | 2 |
| #22608703 | 2 |
| #22608683 | 2 |
| #22608599 | 2 |
| C2×#17988331 | 2 |
| #22607805 | 2 |
| C73×#1965 | 2 |
| #10607 | 73 |