Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
326 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 104 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. #22626288 | C2 | semidirect |
| 2. C4×#14556665 | C2 | semidirect |
| 3. Q8⋊#11924031 | C2 | semidirect |
| 4. D4⋊#11924031 | C2 | semidirect |
| 144. C73 | #11614 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626288 | 2 |
| C4×#14556665 | 2 |
| Q8⋊#11924031 | 2 |
| D4⋊#11924031 | 2 |
| #22618907 | 2 |
| #11614 | 73 |