Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
508 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 132 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. C23×#11924031 | C2 | semidirect |
| 2. C2×#17989485 | C2 | semidirect |
| 3. #22626158 | C2 | semidirect |
| 4. #22624985 | C2 | semidirect |
| 27. C2×#11924031 | D4 | semidirect |
| 125. C22×C73 | #350 | semidirect |
| 145. C73 | #12983 | semidirect |
| 265. C22 | #17989485 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11924031 | 2 |
| C2×#17989485 | 2 |
| #22626158 | 2 |
| #22624985 | 2 |
| #22618626 | 2 |
| #12983 | 73 |