Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
880 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 880 conjugacy classes of subgroups — too many to draw. Only its 229 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×#17984799 | C2 | semidirect |
| 3. C2×C4⋊C4×D139 | C2 | semidirect |
| 4. #22580859 | C2 | semidirect |
| 5. #22580858 | C2 | semidirect |
| 6. #22580856 | C2 | semidirect |
| 7. #22580829 | C2 | semidirect |
| 8. #22580811 | C2 | semidirect |
| 9. #390×C139 | C2 | semidirect |
| 12. C2×#14555784 | C4 | semidirect |
| 36. C2×Dic278 | C2×C4 | semidirect |
| 42. C22×Dic139 | C2×C4 | semidirect |
| 61. C2×D4×C139 | C2×C4 | semidirect |
| 88. C4×D139 | C22⋊C4 | semidirect |
| 133. C139 | #2311 | semidirect |
| 141. #390 | D139 | semidirect |
| 177. C2×D4 | C4×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555784 | 2 |
| C2×#17984799 | 2 |
| C2×C4⋊C4×D139 | 2 |
| #22580859 | 2 |
| #22580858 | 2 |
| #22580856 | 2 |
| #22580829 | 2 |
| #22580811 | 2 |
| #390×C139 | 2 |
| #2311 | 139 |