Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
258 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 1. #22627140 | C2 | semidirect |
| 2. #22626995 | C2 | semidirect |
| 3. #22626974 | C2 | semidirect |
| 4. C8×#11924040 | C2 | semidirect |
| 34. #11924040 | D8 | semidirect |
| 43. D584 | C16 | semidirect |
| 55. D292 | C2×C16 | semidirect |
| 63. C8×C73 | C2×C16 | semidirect |
| 85. C73 | C16×D8 | semidirect |
| 144. C8 | #14556686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627140 | 2 |
| #22626995 | 2 |
| #22626974 | 2 |
| C8×#11924040 | 2 |
| #22625512 | 2 |
| C16×D8 | 73 |