Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
402 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 12. C2×#14556537 | C4 | semidirect |
| 162. C73 | #13244 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556537 | 2 |
| C2×#17988416 | 2 |
| C2×#17988404 | 2 |
| #22611530 | 2 |
| #22610847 | 2 |
| #22610844 | 2 |
| C2×#362×C73 | 2 |
| #13244 | 73 |