Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
560 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 88 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. #22626675 | C2 | semidirect |
| 2. #22626073 | C2 | semidirect |
| 3. #22625443 | C2 | semidirect |
| 4. C2×#17989445 | C2 | semidirect |
| 5. #22624822 | C2 | semidirect |
| 6. #22624775 | C2 | semidirect |
| 99. #11924037 | D8 | semidirect |
| 276. C73 | #9273 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626675 | 2 |
| #22626073 | 2 |
| #22625443 | 2 |
| C2×#17989445 | 2 |
| #22624822 | 2 |
| #22624775 | 2 |
| #22620847 | 2 |
| #9273 | 73 |