Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
184 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 57 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×#17984788 | C2 | semidirect |
| 2. C2×#17984786 | C2 | semidirect |
| 3. C2×#17984785 | C2 | semidirect |
| 5. #22581337 | C2 | semidirect |
| 6. C4×C139⋊C16 | C2 | semidirect |
| 7. #495×C139 | C2 | semidirect |
| 75. C139 | #2249 | semidirect |
| 82. #495 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984788 | 2 |
| C2×#17984786 | 2 |
| C2×#17984785 | 2 |
| C2×#17984783 | 2 |
| #22581337 | 2 |
| C4×C139⋊C16 | 2 |
| #495×C139 | 2 |
| #2249 | 139 |