Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
440 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 440 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. #22611603 | C2 | semidirect |
| 2. #22611581 | C2 | semidirect |
| 3. #22610479 | C2 | semidirect |
| 4. #22610459 | C2 | semidirect |
| 5. #22610216 | C2 | semidirect |
| 6. #22608060 | C2 | semidirect |
| 209. C73 | #13432 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22611603 | 2 |
| #22611581 | 2 |
| #22610479 | 2 |
| #22610459 | 2 |
| #22610216 | 2 |
| #22608060 | 2 |
| C73×#3199 | 2 |
| #13432 | 73 |