Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
346 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 59. #14556510 | C8 | semidirect |
| 60. #14556509 | C8 | semidirect |
| 61. #14556509 | C8 | semidirect |
| 62. #101×C73 | C8 | semidirect |
| 175. C73 | #9549 | semidirect |
| 219. #101 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627056 | 2 |
| #22627052 | 2 |
| C2×Q8⋊#10596842 | 2 |
| M16×#10596842 | 2 |
| #22626943 | 2 |
| #22626938 | 2 |
| #101×#64408 | 2 |
| #9549 | 73 |