Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
238 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 82 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. Q16×#10596833 | C2 | semidirect |
| 3. #22624962 | C2 | semidirect |
| 4. #22624887 | C2 | semidirect |
| 6. #22624842 | C2 | semidirect |
| 42. SD32×C73 | C8 | semidirect |
| 63. Q16×C73 | C2×C8 | semidirect |
| 67. C16×C73 | C2×C8 | semidirect |
| 113. C73 | #12043 | semidirect |
| 134. SD32 | #10596833 | semidirect |
| 154. Q16 | C2×#10596833 | semidirect |
| 173. C16 | C2×#10596833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×#10596833 | 2 |
| D8×#10596833 | 2 |
| #22624962 | 2 |
| #22624887 | 2 |
| #22624885 | 2 |
| #22624842 | 2 |
| SD32×Dic73 | 2 |
| #12043 | 73 |