Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
696 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 189 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×#17984830 | C2 | semidirect |
| 2. C2×#17984821 | C2 | semidirect |
| 4. #22580859 | C2 | semidirect |
| 5. #22580855 | C2 | semidirect |
| 6. #22580844 | C2 | semidirect |
| 7. #22580832 | C2 | semidirect |
| 8. #22580819 | C2 | semidirect |
| 9. C22×C42×C139 | C2 | semidirect |
| 63. C42×C139 | D4 | semidirect |
| 103. C22×C139 | #124 | semidirect |
| 128. C139 | #2850 | semidirect |
| 133. C22×C42 | D139 | semidirect |
| 192. C42 | C22⋊D139 | semidirect |
| 237. C22 | #17984830 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984830 | 2 |
| C2×#17984821 | 2 |
| C2×#17984816 | 2 |
| #22580859 | 2 |
| #22580855 | 2 |
| #22580844 | 2 |
| #22580832 | 2 |
| #22580819 | 2 |
| C22×C42×C139 | 2 |
| #2850 | 139 |