Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
706 conjugacy classes of subgroups; only the 297 normal subgroups are shown.
This group has 706 conjugacy classes of subgroups — too many to draw. Only its 297 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. #22627123 | C2 | semidirect |
| 3. #22627120 | C2 | semidirect |
| 4. #22627117 | C2 | semidirect |
| 92. C4×C73 | #504 | semidirect |
| 107. C73 | #33398 | semidirect |
| 198. C4 | #17989709 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989709 | 2 |
| #22627123 | 2 |
| #22627120 | 2 |
| #22627117 | 2 |
| C4×#14556679 | 2 |
| #33398 | 73 |