Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
414 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 57. #14556516 | C8 | semidirect |
| 58. #14556515 | C8 | semidirect |
| 59. #14556514 | C8 | semidirect |
| 60. #103×C73 | C8 | semidirect |
| 197. C73 | #9553 | semidirect |
| 243. #103 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| (C2×#10596842)⋊Q8 | 2 |
| #22627080 | 2 |
| C2×Q8⋊#10596842 | 2 |
| C2×C8×#10596842 | 2 |
| #22626939 | 2 |
| #22626937 | 2 |
| #103×#64408 | 2 |
| #9553 | 73 |