Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
484 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 229 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 |
|---|---|---|
| 8. #17984834 | C4 | direct (N × H) |
| 68. C4×C139 | #125 | semidirect |
| 76. C139 | C4×#125 | semidirect |
| 147. C4 | #17984834 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984834 | 2 |
| #22580851 | 2 |
| #22580837 | 2 |
| #22580819 | 2 |
| C4×Dic139⋊C4 | 2 |
| C4×C4⋊Dic139 | 2 |
| C43×C139 | 2 |
| C4×#125 | 139 |