Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
380 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 115 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. C2×#17988416 | C2 | semidirect |
| 4. #22610721 | C2 | semidirect |
| 5. #22608042 | C2 | semidirect |
| 6. #22608020 | C2 | semidirect |
| 15. #17988394 | C4 | semidirect |
| 148. C73 | #12947 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988416 | 2 |
| #22611659 | 2 |
| C2×#17988394 | 2 |
| #22610721 | 2 |
| #22608042 | 2 |
| #22608020 | 2 |
| C73×#2957 | 2 |
| #12947 | 73 |