Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
350 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 120 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. #22624949 | C2 | direct (N × H) |
| 115. C2×C73 | #1364 | semidirect |
| 123. C73 | C2×#1364 | semidirect |
| 233. C2 | #22624949 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989508 | 2 |
| C2×#17989451 | 2 |
| #22624949 | 2 |
| C2×#17988991 | 2 |
| C2×#1364 | 73 |