Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
364 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 73 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. #22627107 | C2 | semidirect |
| 2. #22626971 | C2 | semidirect |
| 3. #22626963 | C2 | semidirect |
| 132. C73 | #11486 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627107 | 2 |
| #22626971 | 2 |
| #22626963 | 2 |
| #22626657 | 2 |
| #11486 | 73 |