Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
572 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 141 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×#17984865 | C2 | semidirect |
| 2. C2×#17984863 | C2 | semidirect |
| 3. C2×#17984861 | C2 | semidirect |
| 4. #22581502 | C2 | semidirect |
| 5. #22581337 | C2 | semidirect |
| 6. #22581335 | C2 | semidirect |
| 7. #22581331 | C2 | semidirect |
| 8. #22581328 | C2 | semidirect |
| 9. #22581324 | C2 | semidirect |
| 10. C4×C8×D139 | C2 | semidirect |
| 11. #495×C139 | C2 | semidirect |
| 62. C8×D139 | D4 | semidirect |
| 63. C8×D139 | D4 | semidirect |
| 119. Dic139 | #135 | semidirect |
| 125. C139 | #3147 | semidirect |
| 133. #495 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984865 | 2 |
| C2×#17984863 | 2 |
| C2×#17984861 | 2 |
| #22581502 | 2 |
| #22581337 | 2 |
| #22581335 | 2 |
| #22581331 | 2 |
| #22581328 | 2 |
| #22581324 | 2 |
| C4×C8×D139 | 2 |
| #495×C139 | 2 |
| #3147 | 139 |