Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
622 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 622 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 2. #22619403 | C2 | semidirect |
| 3. #22614836 | C2 | semidirect |
| 4. #22608492 | C2 | semidirect |
| 5. #22608357 | C2 | semidirect |
| 6. #22607790 | C2 | semidirect |
| 7. C73×#1479 | C2 | semidirect |
| 132. C2×Q8×C73 | D8 | semidirect |
| 249. #1479 | D73 | semidirect |
| 251. C73 | #9997 | semidirect |
| 341. C2×Q8 | D584 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619932 | 2 |
| #22619403 | 2 |
| #22614836 | 2 |
| #22608492 | 2 |
| #22608357 | 2 |
| #22607790 | 2 |
| C73×#1479 | 2 |
| #9997 | 73 |