Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
374 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 33. #14556662 | C8 | semidirect |
| 34. #14556661 | C8 | semidirect |
| 43. #14556527 | C8 | semidirect |
| 44. #14556526 | C8 | semidirect |
| 45. #108×C73 | C8 | semidirect |
| 86. #10596842 | #108 | direct (N × H) |
| 126. C73 | C8×#108 | semidirect |
| 152. #108 | #10596842 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627055 | 2 |
| M16×#10596842 | 2 |
| C2×C8×#10596842 | 2 |
| #22626938 | 2 |
| #108×#64408 | 2 |
| C8×#108 | 73 |