Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
402 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 93 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. #64408⋊M32 | C2 | semidirect |
| 2. C2×#17989676 | C2 | semidirect |
| 3. #22626980 | C2 | semidirect |
| 4. #22626979 | C2 | semidirect |
| 52. #14556614 | C8 | semidirect |
| 53. #14556613 | C8 | semidirect |
| 56. #14556610 | C8 | semidirect |
| 61. #135×C73 | C8 | semidirect |
| 97. Dic292 | C2×C8 | semidirect |
| 102. D584 | C2×C8 | semidirect |
| 110. Q16×C73 | C2×C8 | semidirect |
| 112. D8×C73 | C2×C8 | semidirect |
| 188. C73 | #11598 | semidirect |
| 212. #135 | #10596842 | semidirect |
| 262. Q16 | C2×#10596842 | semidirect |
| 269. D8 | C2×#10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #64408⋊M32 | 2 |
| C2×#17989676 | 2 |
| #22626980 | 2 |
| #22626979 | 2 |
| #135×#64408 | 2 |
| #11598 | 73 |