Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
438 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 110 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. #22626158 | C2 | semidirect |
| 2. #22624867 | C2 | semidirect |
| 3. #22624851 | C2 | semidirect |
| 89. C23×C73 | M32 | semidirect |
| 108. C2×C4×C73 | M32 | semidirect |
| 150. C73 | #11466 | semidirect |
| 235. C23 | #14556665 | semidirect |
| 254. C2×C4 | #14556665 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626158 | 2 |
| #22624867 | 2 |
| #22624851 | 2 |
| C2×D4×#10596831 | 2 |
| #11466 | 73 |