Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
382 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 3. #22626986 | C2 | semidirect |
| 4. Q8⋊#11924040 | C2 | semidirect |
| 71. Q8×D73 | C16 | semidirect |
| 95. Q8×C73 | C2×C16 | semidirect |
| 115. Dic146 | C2×C16 | semidirect |
| 143. D73 | Q8⋊C16 | semidirect |
| 149. C73 | C2×Q8⋊C16 | semidirect |
| 242. Q8 | #14556686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627117 | 2 |
| C4×#14556686 | 2 |
| #22626986 | 2 |
| Q8⋊#11924040 | 2 |
| Q8×#11924036 | 2 |
| C2×Q8⋊C16 | 73 |