Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
456 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 129 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. #22581500 | C2 | semidirect |
| 2. #22581357 | C2 | semidirect |
| 3. #22581328 | C2 | semidirect |
| 4. #22581298 | C2 | semidirect |
| 5. #22581190 | C2 | semidirect |
| 6. #22581188 | C2 | semidirect |
| 7. #22581186 | C2 | semidirect |
| 8. C4×D1112 | C2 | semidirect |
| 9. C4×#14555770 | C2 | semidirect |
| 10. C4×C8×D139 | C2 | semidirect |
| 11. C4×D8×C139 | C2 | semidirect |
| 89. C4×D139 | D8 | semidirect |
| 91. C139⋊C8 | #41 | semidirect |
| 101. C8×C139 | #41 | semidirect |
| 127. C139 | #3169 | semidirect |
| 138. C4×D8 | D139 | semidirect |
| 229. C8 | #14555785 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581500 | 2 |
| #22581357 | 2 |
| #22581328 | 2 |
| #22581298 | 2 |
| #22581190 | 2 |
| #22581188 | 2 |
| #22581186 | 2 |
| C4×D1112 | 2 |
| C4×#14555770 | 2 |
| C4×C8×D139 | 2 |
| C4×D8×C139 | 2 |
| #3169 | 139 |