Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
454 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 134 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. C2×C22⋊#11924031 | C2 | semidirect |
| 2. #22624867 | C2 | semidirect |
| 3. #22624851 | C2 | semidirect |
| 61. C2×D4×C73 | C16 | semidirect |
| 88. C23×C73 | C2×C16 | semidirect |
| 108. C2×C4×C73 | C2×C16 | semidirect |
| 150. C73 | #11465 | semidirect |
| 193. C2×D4 | #11924031 | semidirect |
| 234. C23 | C2×#11924031 | semidirect |
| 254. C2×C4 | C2×#11924031 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊#11924031 | 2 |
| #22624867 | 2 |
| #22624851 | 2 |
| C2×D4×#10596831 | 2 |
| #11465 | 73 |