Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
230 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 77 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. C2×C4×C139⋊C8 | C2 | semidirect |
| 3. #22580683 | C2 | semidirect |
| 4. #22580680 | C2 | semidirect |
| 5. #432×C139 | C2 | semidirect |
| 90. C139 | #1494 | semidirect |
| 93. #432 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581487 | 2 |
| C2×C4×C139⋊C8 | 2 |
| #22580683 | 2 |
| #22580680 | 2 |
| #432×C139 | 2 |
| #1494 | 139 |