Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
170 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 1. C2×#17984786 | C2 | semidirect |
| 3. #22581337 | C2 | semidirect |
| 4. C4⋊(C139⋊C16) | C2 | semidirect |
| 5. #22580756 | C2 | semidirect |
| 6. #22580753 | C2 | semidirect |
| 7. C4×D8×C139 | C2 | semidirect |
| 76. C139 | #2210 | semidirect |
| 81. C4×D8 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984786 | 2 |
| C2×#17984783 | 2 |
| #22581337 | 2 |
| C4⋊(C139⋊C16) | 2 |
| #22580756 | 2 |
| #22580753 | 2 |
| C4×D8×C139 | 2 |
| #2210 | 139 |