Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
412 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 149 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. #22581510 | C2 | semidirect |
| 3. #22581351 | C2 | semidirect |
| 4. #22581326 | C2 | semidirect |
| 5. #22581304 | C2 | semidirect |
| 6. #22581300 | C2 | semidirect |
| 7. #22581182 | C2 | semidirect |
| 8. C4×#14555774 | C2 | semidirect |
| 9. C2×C4×C8×C139 | C2 | semidirect |
| 82. C2×C4×C139 | SD16 | semidirect |
| 90. C8×C139 | #41 | semidirect |
| 112. C139 | #3167 | semidirect |
| 122. C2×C4×C8 | D139 | semidirect |
| 195. C2×C4 | #14555774 | semidirect |
| 203. C8 | #14555785 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581510 | 2 |
| #22581503 | 2 |
| #22581351 | 2 |
| #22581326 | 2 |
| #22581304 | 2 |
| #22581300 | 2 |
| #22581182 | 2 |
| C4×#14555774 | 2 |
| C2×C4×C8×C139 | 2 |
| #3167 | 139 |