Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
270 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 105 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. #22626990 | C2 | semidirect |
| 3. #22626989 | C2 | semidirect |
| 76. C8×C73 | M32 | semidirect |
| 78. #10596831 | M32 | semidirect |
| 100. C73 | #11996 | semidirect |
| 174. C8 | #14556687 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627119 | 2 |
| #22626990 | 2 |
| #22626989 | 2 |
| C2×C8×#10596833 | 2 |
| #11996 | 73 |