Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
378 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 112 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. #22626291 | C2 | semidirect |
| 2. C4×#14556664 | C2 | semidirect |
| 3. Q8⋊#11924031 | C2 | semidirect |
| 4. #22624882 | C2 | semidirect |
| 58. #11924029 | C16 | semidirect |
| 95. Q8×C73 | C2×C16 | semidirect |
| 107. D292 | C2×C16 | semidirect |
| 152. C73 | #11613 | semidirect |
| 242. Q8 | #14556664 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626291 | 2 |
| C4×#14556664 | 2 |
| Q8⋊#11924031 | 2 |
| #22624882 | 2 |
| C8×#11924029 | 2 |
| #11613 | 73 |