Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
398 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 3. #22608701 | C2 | semidirect |
| 4. #22608495 | C2 | semidirect |
| 6. #22607790 | C2 | semidirect |
| 7. C73×#1542 | C2 | semidirect |
| 176. #1542 | D73 | semidirect |
| 180. C73 | #10468 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619724 | 2 |
| #22609942 | 2 |
| #22608701 | 2 |
| #22608495 | 2 |
| #22608251 | 2 |
| #22607790 | 2 |
| C73×#1542 | 2 |
| #10468 | 73 |