Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
290 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 128 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. #22624845 | C2 | semidirect |
| 4. #22624842 | C2 | semidirect |
| 41. #11924031 | M16 | semidirect |
| 95. C73 | #11408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989473 | 2 |
| C8×#11924037 | 2 |
| #22624845 | 2 |
| #22624842 | 2 |
| #22611727 | 2 |
| #11408 | 73 |