Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
368 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 88 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. C4×#14556666 | C2 | semidirect |
| 2. #22625486 | C2 | semidirect |
| 3. #22624889 | C2 | semidirect |
| 125. C73 | #11680 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556666 | 2 |
| #22625486 | 2 |
| #22624889 | 2 |
| #22620508 | 2 |
| #11680 | 73 |