Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
1212 conjugacy classes of subgroups; only the 509 normal subgroups are shown.
This group has 1212 conjugacy classes of subgroups — too many to draw. Only its 509 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C42 | C22×D139 |
| commutator, socle, cosocle | C22×C139 | C25 |
| Frattini | C22 | C24×D139 |
| Fitting | C22×C42×C139 | C2 |
| hypercenter | C22×C42 | D139 |
| hypocenter | C139 | #3444 |
| LCS | G ▷ C22×C139 ▷ C139 | |
| UCS | C1 ◁ C42 ◁ C22×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22581510 | C2 | semidirect |
| 2. #22581503 | C2 | semidirect |
| 3. #22581487 | C2 | semidirect |
| 4. #22581464 | C2 | semidirect |
| 5. C4×#14555785 | C2 | semidirect |
| 6. C22×C42×C139 | C2 | semidirect |
| 8. #17984842 | C22 | semidirect |
| 9. #17984839 | C22 | semidirect |
| 10. #17984836 | C22 | semidirect |
| 11. #17984834 | C22 | semidirect |
| 12. #17984830 | C22 | semidirect |
| 17. C4×Dic278 | C22 | semidirect |
| 18. C4×D556 | C22 | semidirect |
| 21. #17984799 | C22 | semidirect |
| 22. C42×D139 | C22 | semidirect |
| 60. C2×C4×C139 | #41 | semidirect |
| 76. C139 | #3444 | semidirect |
| 83. C22×C42 | D139 | semidirect |
| 137. C2×C4 | #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 |
| #22581487 | 2 |
| #22581464 | 2 |
| C4×#14555785 | 2 |
| C22×C42×C139 | 2 |
| #3444 | 139 |