Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
372 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 52. #14556523 | C8 | semidirect |
| 53. #14556522 | C8 | semidirect |
| 54. #14556522 | C8 | semidirect |
| 55. #106×C73 | C8 | semidirect |
| 180. C73 | #9534 | semidirect |
| 214. #106 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627080 | 2 |
| C4⋊C4×#10596842 | 2 |
| #22626939 | 2 |
| #22626937 | 2 |
| (C2×#10596842)⋊C8 | 2 |
| #106×#64408 | 2 |
| #9534 | 73 |