Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
1536 conjugacy classes of subgroups; only the 549 normal subgroups are shown.
This group has 1536 conjugacy classes of subgroups — too many to draw. Only its 549 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D139 |
| commutator, socle, cosocle | C22×C139 | C25 |
| Fitting | C22×#41×C139 | C2 |
| hypercenter | C22×#41 | D139 |
| hypocenter | C139 | #3487 |
| LCS | G ▷ C22×C139 ▷ C139 | |
| UCS | C1 ◁ C22 ◁ C22×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#17984890 | C2 | semidirect |
| 2. #22581622 | C2 | semidirect |
| 3. #22581610 | C2 | semidirect |
| 4. #22581520 | C2 | semidirect |
| 5. #22581464 | C2 | semidirect |
| 6. #22581431 | C2 | semidirect |
| 7. C22×#41×C139 | C2 | semidirect |
| 9. C2×#14555786 | C22 | semidirect |
| 11. C2×Q8×D139 | C22 | semidirect |
| 12. #17984838 | C22 | semidirect |
| 13. #17984829 | C22 | semidirect |
| 15. #17984821 | C22 | semidirect |
| 16. #17984816 | C22 | semidirect |
| 17. #17984813 | C22 | semidirect |
| 19. Q8×Dic139 | C22 | semidirect |
| 20. C4×C22⋊D139 | C22 | semidirect |
| 43. C2×Q8×C139 | D4 | semidirect |
| 87. C139 | #3487 | semidirect |
| 90. C22×#41 | D139 | semidirect |
| 121. C2×Q8 | C22⋊D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984890 | 2 |
| #22581622 | 2 |
| #22581610 | 2 |
| #22581520 | 2 |
| #22581464 | 2 |
| #22581431 | 2 |
| C22×#41×C139 | 2 |
| #3487 | 139 |