Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
692 conjugacy classes of subgroups; only the 225 normal subgroups are shown.
This group has 692 conjugacy classes of subgroups — too many to draw. Only its 225 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 |
|---|---|---|
| 36. #14556583 | C8 | semidirect |
| 37. #14556582 | C8 | semidirect |
| 38. #14556581 | C8 | semidirect |
| 42. #125×C73 | C8 | semidirect |
| 125. C73 | #23263 | semidirect |
| 146. #125 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627078 | 2 |
| C4⋊C4×#10596842 | 2 |
| #22627065 | 2 |
| #125×#64408 | 2 |
| #23263 | 73 |