Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
454 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 454 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 |
|---|---|---|
| 25. #14556652 | C8 | direct (N × H) |
| 109. C8×C73 | #101 | semidirect |
| 137. C73 | C8×#101 | semidirect |
| 243. C8 | #14556652 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556652 | 2 |
| #22625173 | 2 |
| C8×#11924037 | 2 |
| #22624776 | 2 |
| C2×C8×Dic146 | 2 |
| C8×#101 | 73 |