Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
232 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 2. #22609301 | C2 | semidirect |
| 4. #22608005 | C2 | semidirect |
| 5. #22607981 | C2 | semidirect |
| 7. Q8×C16×C73 | C2 | semidirect |
| 70. C16×C73 | SD16 | semidirect |
| 73. Q8×C73 | SD32 | semidirect |
| 111. Q8×C16 | D73 | semidirect |
| 117. C73 | #12441 | semidirect |
| 180. C16 | #11924015 | semidirect |
| 185. Q8 | #14556536 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612187 | 2 |
| #22609301 | 2 |
| #22609291 | 2 |
| #22608005 | 2 |
| #22607981 | 2 |
| #22607978 | 2 |
| Q8×C16×C73 | 2 |
| #12441 | 73 |