Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
354 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 173 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. #22626947 | C2 | semidirect |
| 3. C8×#11924040 | C2 | semidirect |
| 15. #14556687 | C8 | direct (N × H) |
| 32. #11924040 | C2×C8 | semidirect |
| 65. #10596833 | M32 | semidirect |
| 68. C8×C73 | M32 | semidirect |
| 70. #10596831 | M32 | semidirect |
| 91. C73 | C8×M32 | semidirect |
| 157. C8 | #14556687 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556687 | 2 |
| #22626947 | 2 |
| C8×#11924040 | 2 |
| C2×C8×#10596833 | 2 |
| C8×M32 | 73 |