Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
588 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 97 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. #22580969 | C2 | semidirect |
| 3. #22580959 | C2 | semidirect |
| 4. #22580927 | C2 | semidirect |
| 5. #413×C139 | C2 | semidirect |
| 9. C2×#14555785 | C4 | semidirect |
| 11. C22×D556 | C4 | semidirect |
| 15. #17984801 | C22 | semidirect |
| 20. C2×M16×C139 | C22 | semidirect |
| 114. C139 | #1795 | semidirect |
| 119. #413 | D139 | semidirect |
| 131. C2×M16 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984888 | 2 |
| #22580969 | 2 |
| #22580959 | 2 |
| #22580927 | 2 |
| #413×C139 | 2 |
| #1795 | 139 |