Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
322 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 141 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. #22626949 | C2 | semidirect |
| 3. #22626948 | C2 | semidirect |
| 65. #10596833 | M32 | semidirect |
| 68. C8×C73 | M32 | semidirect |
| 70. #10596831 | M32 | semidirect |
| 91. C73 | #11402 | semidirect |
| 157. C8 | #14556687 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556687 | 2 |
| #22626949 | 2 |
| #22626948 | 2 |
| C2×C8×#10596833 | 2 |
| #11402 | 73 |