Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
532 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 221 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. #22627146 | C2 | semidirect |
| 3. #22627131 | C2 | semidirect |
| 4. #22627120 | C2 | semidirect |
| 61. Q8×C73 | M32 | semidirect |
| 99. C73 | #33505 | semidirect |
| 155. Q8 | #14556688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11924040 | 2 |
| #22627146 | 2 |
| #22627131 | 2 |
| #22627120 | 2 |
| #22626737 | 2 |
| #33505 | 73 |