Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
362 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22627130 | C2 | semidirect |
| 2. #22627117 | C2 | semidirect |
| 3. Q8⋊#11924040 | C2 | semidirect |
| 4. #22626974 | C2 | semidirect |
| 70. #11924029 | C16 | semidirect |
| 97. Q8×C73 | C2×C16 | semidirect |
| 109. D292 | C2×C16 | semidirect |
| 155. C73 | #11621 | semidirect |
| 247. Q8 | #14556686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627130 | 2 |
| #22627117 | 2 |
| Q8⋊#11924040 | 2 |
| #22626974 | 2 |
| #22626737 | 2 |
| #11621 | 73 |