Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
444 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 444 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. C4×#14556527 | C2 | semidirect |
| 2. #22608523 | C2 | semidirect |
| 3. #22608348 | C2 | semidirect |
| 4. C8×#11924012 | C2 | semidirect |
| 140. C73 | #9724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556527 | 2 |
| #22608523 | 2 |
| #22608348 | 2 |
| C8×#11924012 | 2 |
| C73×#3169 | 2 |
| #9724 | 73 |