Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
368 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 111 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. #22611730 | C2 | semidirect |
| 2. C4×#14556527 | C2 | semidirect |
| 3. #22607946 | C2 | semidirect |
| 126. C73 | #11747 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22611730 | 2 |
| C4×#14556527 | 2 |
| #22607946 | 2 |
| C73×#3169 | 2 |
| #11747 | 73 |