Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
232 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 102 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. Q8×#11924031 | C2 | semidirect |
| 3. #22624960 | C2 | semidirect |
| 4. Q8⋊#11924031 | C2 | semidirect |
| 6. #22624844 | C2 | semidirect |
| 59. SD16×C73 | C16 | semidirect |
| 70. Q8×C73 | C2×C16 | semidirect |
| 82. C8×C73 | C2×C16 | semidirect |
| 113. C73 | SD16⋊C16 | semidirect |
| 153. SD16 | #11924031 | semidirect |
| 176. Q8 | C2×#11924031 | semidirect |
| 194. C8 | C2×#11924031 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11924031 | 2 |
| D4×#11924031 | 2 |
| #22624960 | 2 |
| Q8⋊#11924031 | 2 |
| D4⋊#11924031 | 2 |
| #22624844 | 2 |
| SD16×#10596831 | 2 |
| SD16⋊C16 | 73 |