Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
494 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 133 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×#17984864 | C2 | semidirect |
| 2. #22581624 | C2 | semidirect |
| 3. #22581608 | C2 | semidirect |
| 4. #22581326 | C2 | semidirect |
| 5. #22581182 | C2 | semidirect |
| 6. #22581164 | C2 | semidirect |
| 7. #22581149 | C2 | semidirect |
| 8. #22581117 | C2 | semidirect |
| 9. #22581100 | C2 | semidirect |
| 10. C4×#14555774 | C2 | semidirect |
| 11. C8×D4×C139 | C2 | semidirect |
| 61. #14555774 | D4 | semidirect |
| 127. C4×C139 | #135 | semidirect |
| 140. C139 | #3284 | semidirect |
| 152. C8×D4 | D139 | semidirect |
| 272. C4 | #17984864 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984864 | 2 |
| #22581624 | 2 |
| #22581608 | 2 |
| #22581326 | 2 |
| #22581182 | 2 |
| #22581164 | 2 |
| #22581149 | 2 |
| #22581117 | 2 |
| #22581100 | 2 |
| C4×#14555774 | 2 |
| C8×D4×C139 | 2 |
| #3284 | 139 |