Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
1492 conjugacy classes of subgroups; only the 557 normal subgroups are shown.
This group has 1492 conjugacy classes of subgroups — too many to draw. Only its 557 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 | C23×Q8×C139 | C2 |
| hypercenter | C23×Q8 | D139 |
| hypocenter | C139 | #3486 |
| LCS | G ▷ C22×C139 ▷ C139 | |
| UCS | C1 ◁ C22 ◁ C23×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#17984890 | C2 | semidirect |
| 2. Q8×C22⋊D139 | C2 | semidirect |
| 3. #22581614 | C2 | semidirect |
| 4. #22581527 | C2 | semidirect |
| 5. #22581464 | C2 | semidirect |
| 6. #22581431 | C2 | semidirect |
| 7. C23×Q8×C139 | C2 | semidirect |
| 9. C2×#14555786 | C22 | semidirect |
| 11. C2×Q8×D139 | C22 | semidirect |
| 12. #17984840 | C22 | semidirect |
| 13. #17984831 | C22 | semidirect |
| 16. #17984818 | C22 | semidirect |
| 19. Q8×Dic139 | C22 | semidirect |
| 44. C2×Q8×C139 | D4 | semidirect |
| 75. C22×C139 | 2−1+4 | semidirect |
| 88. C139 | #3486 | semidirect |
| 91. C23×Q8 | D139 | semidirect |
| 123. C2×Q8 | C22⋊D139 | semidirect |
| 166. C22 | #17984890 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984890 | 2 |
| Q8×C22⋊D139 | 2 |
| #22581614 | 2 |
| #22581527 | 2 |
| #22581464 | 2 |
| #22581431 | 2 |
| C23×Q8×C139 | 2 |
| #3486 | 139 |