Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
246 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 3. #22626995 | C2 | semidirect |
| 4. #22626989 | C2 | semidirect |
| 56. M16×C73 | C16 | semidirect |
| 76. C8×C73 | C2×C16 | semidirect |
| 100. C73 | #12015 | semidirect |
| 135. M16 | #11924040 | semidirect |
| 172. C8 | C2×#11924040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627128 | 2 |
| C2×C4⋊#11924040 | 2 |
| #22626995 | 2 |
| #22626989 | 2 |
| M16×#10596833 | 2 |
| #12015 | 73 |