Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
230 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 2. #22625524 | C2 | semidirect |
| 3. #22624955 | C2 | semidirect |
| 4. #22624891 | C2 | semidirect |
| 6. #22624848 | C2 | semidirect |
| 42. SD32×C73 | C8 | semidirect |
| 62. Q16×C73 | C2×C8 | semidirect |
| 66. C16×C73 | C2×C8 | semidirect |
| 110. C73 | #12065 | semidirect |
| 131. SD32 | #10596833 | semidirect |
| 151. Q16 | C2×#10596833 | semidirect |
| 169. C16 | C2×#10596833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625527 | 2 |
| #22625524 | 2 |
| #22624955 | 2 |
| #22624891 | 2 |
| #22624889 | 2 |
| #22624848 | 2 |
| #22611796 | 2 |
| #12065 | 73 |