Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
246 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 246 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 |
|---|---|---|
| 1. #22625527 | C2 | semidirect |
| 2. #22624955 | C2 | semidirect |
| 3. #22624889 | C2 | semidirect |
| 4. #22624847 | C2 | semidirect |
| 27. D16×C73 | C8 | semidirect |
| 41. D8×C73 | C2×C8 | semidirect |
| 43. C16×C73 | C2×C8 | semidirect |
| 74. C73 | #12067 | semidirect |
| 88. D16 | #10596833 | semidirect |
| 101. D8 | C2×#10596833 | semidirect |
| 112. 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 |
| #22624955 | 2 |
| #22624889 | 2 |
| #22624847 | 2 |
| #22611807 | 2 |
| #12067 | 73 |