Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
374 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 140 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 |
|---|---|---|
| 23. #14556662 | C8 | semidirect |
| 81. #10596833 | #108 | semidirect |
| 110. C73 | C8×#108 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556662 | 2 |
| #22625133 | 2 |
| C8×#11924036 | 2 |
| #22624762 | 2 |
| #22608678 | 2 |
| C8×#108 | 73 |