Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
792 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 202 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. #22626104 | C2 | semidirect |
| 2. #22626000 | C2 | semidirect |
| 4. #22625673 | C2 | semidirect |
| 5. #22625646 | C2 | semidirect |
| 86. C4×Dic73 | M16 | semidirect |
| 163. C73 | #23272 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626104 | 2 |
| #22626000 | 2 |
| #22625908 | 2 |
| #22625673 | 2 |
| #22625646 | 2 |
| #22612478 | 2 |
| #23272 | 73 |