Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
338 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 79 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. #22612156 | C2 | semidirect |
| 3. #22609291 | C2 | semidirect |
| 4. #22607986 | C2 | semidirect |
| 5. Q8⋊#11924003 | C2 | semidirect |
| 6. #22607892 | C2 | semidirect |
| 7. Q8×D8×C73 | C2 | semidirect |
| 72. D8×C73 | SD16 | semidirect |
| 92. Q8×C73 | D16 | semidirect |
| 137. Q8×D8 | D73 | semidirect |
| 144. C73 | #12352 | semidirect |
| 206. D8 | #11924015 | semidirect |
| 229. Q8 | #14556532 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612156 | 2 |
| #22611966 | 2 |
| #22609291 | 2 |
| #22607986 | 2 |
| Q8⋊#11924003 | 2 |
| #22607892 | 2 |
| Q8×D8×C73 | 2 |
| #12352 | 73 |