Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
454 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 40. #14556652 | C8 | semidirect |
| 45. #14556510 | C8 | semidirect |
| 46. #14556509 | C8 | semidirect |
| 47. #101×C73 | C8 | semidirect |
| 92. #10596842 | #101 | direct (N × H) |
| 132. C73 | C8×#101 | semidirect |
| 166. #101 | #10596842 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#10596842 | 2 |
| #22627046 | 2 |
| M16×#10596842 | 2 |
| #22626943 | 2 |
| #101×#64408 | 2 |
| C8×#101 | 73 |