Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
348 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 109 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×#17984765 | C2 | semidirect |
| 4. C2×C8×Dic139 | C2 | semidirect |
| 5. #22580858 | C2 | semidirect |
| 7. C2×#106×C139 | C2 | semidirect |
| 12. C2×#14555774 | C4 | semidirect |
| 74. C2×Dic139 | SD16 | semidirect |
| 87. C8×C139 | C22⋊C4 | semidirect |
| 112. C139 | #1968 | semidirect |
| 115. C2×#106 | D139 | semidirect |
| 200. C8 | (C2×D139)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555774 | 2 |
| C2×#17984765 | 2 |
| C2×#17984762 | 2 |
| C2×C8×Dic139 | 2 |
| #22580858 | 2 |
| #22580854 | 2 |
| C2×#106×C139 | 2 |
| #1968 | 139 |