Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
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×D109 |
| commutator, socle, cosocle | C22×C109 | C25 |
| Fitting | C22×#41×C109 | C2 |
| hypercenter | C22×#41 | D109 |
| hypocenter | C109 | #3487 |
| LCS | G ▷ C22×C109 ▷ C109 | |
| UCS | C1 ◁ C22 ◁ C22×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#16812747 | C2 | semidirect |
| 2. #20295695 | C2 | semidirect |
| 3. #20295683 | C2 | semidirect |
| 4. #20295593 | C2 | semidirect |
| 5. #20295537 | C2 | semidirect |
| 6. #20295504 | C2 | semidirect |
| 7. C22×#41×C109 | C2 | semidirect |
| 9. C2×#13182030 | C22 | semidirect |
| 11. C2×Q8×D109 | C22 | semidirect |
| 12. #16812695 | C22 | semidirect |
| 13. #16812686 | C22 | semidirect |
| 15. #16812678 | C22 | semidirect |
| 16. #16812673 | C22 | semidirect |
| 17. #16812670 | C22 | semidirect |
| 19. Q8×Dic109 | C22 | semidirect |
| 20. C4×C22⋊D109 | C22 | semidirect |
| 43. C2×Q8×C109 | D4 | semidirect |
| 88. C109 | #3487 | semidirect |
| 90. C22×#41 | D109 | semidirect |
| 121. C2×Q8 | C22⋊D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812747 | 2 |
| #20295695 | 2 |
| #20295683 | 2 |
| #20295593 | 2 |
| #20295537 | 2 |
| #20295504 | 2 |
| C22×#41×C109 | 2 |
| #3487 | 109 |