Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
232 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 86 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. #22624961 | C2 | semidirect |
| 4. Q8⋊#11924031 | C2 | semidirect |
| 6. #22624846 | C2 | semidirect |
| 51. #11924015 | C16 | semidirect |
| 70. Q8×C73 | C2×C16 | semidirect |
| 86. #10596831 | C2×C16 | semidirect |
| 113. C73 | SD16⋊C16 | semidirect |
| 176. Q8 | #14556664 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11924031 | 2 |
| #22626310 | 2 |
| #22624961 | 2 |
| Q8⋊#11924031 | 2 |
| #22624882 | 2 |
| #22624846 | 2 |
| #22608728 | 2 |
| SD16⋊C16 | 73 |