Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
522 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 522 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 |
|---|---|---|
| 2. #22624759 | C2 | semidirect |
| 3. #22624755 | C2 | semidirect |
| 40. C2×C42×C73 | C8 | semidirect |
| 141. C73 | #8730 | semidirect |
| 172. C2×C42 | #10596833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625162 | 2 |
| #22624759 | 2 |
| #22624755 | 2 |
| C4×#14556550 | 2 |
| #8730 | 73 |