Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
532 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 219 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×#11924040 | C2 | semidirect |
| 2. #22627147 | C2 | semidirect |
| 3. #22627129 | C2 | semidirect |
| 4. #22627119 | C2 | semidirect |
| 61. Q8×C73 | M32 | semidirect |
| 99. C73 | #33505 | semidirect |
| 155. Q8 | #14556687 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11924040 | 2 |
| #22627147 | 2 |
| #22627129 | 2 |
| #22627119 | 2 |
| #41×#10596833 | 2 |
| #33505 | 73 |