Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
426 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 45. #14556583 | C8 | semidirect |
| 46. #14556582 | C8 | semidirect |
| 47. #14556582 | C8 | semidirect |
| 55. #125×C73 | C8 | semidirect |
| 184. C73 | #7585 | semidirect |
| 209. #125 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627074 | 2 |
| C4×C4⋊#10596842 | 2 |
| #22626931 | 2 |
| #125×#64408 | 2 |
| #7585 | 73 |