Finite Group DatabasebetaFinite Group DatabasebetaOrder 22336.
334 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 111 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 | C23×D349 |
| commutator, socle, cosocle | C22×C349 | C24 |
| Fitting | #117×C349 | C2 |
| hypercenter | #117 | D349 |
| hypocenter | C349 | #535 |
| LCS | G ▷ C22×C349 ▷ C349 | |
| UCS | C1 ◁ C22 ◁ #117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#19150233 | C2 | semidirect |
| 2. C22×D1396 | C2 | semidirect |
| 3. #26013636 | C2 | semidirect |
| 4. #26013627 | C2 | semidirect |
| 5. #26013614 | C2 | semidirect |
| 6. #26013609 | C2 | semidirect |
| 7. #117×C349 | C2 | semidirect |
| 10. C2×Dic698 | C22 | semidirect |
| 14. C2×D1396 | C22 | semidirect |
| 15. C2×D1396 | C22 | semidirect |
| 17. C2×C4×D349 | C22 | semidirect |
| 18. #19150210 | C22 | semidirect |
| 20. C4⋊C4×C349 | C22 | semidirect |
| 22. C42×C349 | C22 | semidirect |
| 36. C2×C4×C349 | D4 | semidirect |
| 57. C349 | #535 | semidirect |
| 65. #117 | D349 | semidirect |
| 77. C4⋊C4 | C2×D349 | semidirect |
| 80. C42 | C2×D349 | semidirect |
| 94. C2×C4 | D1396 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19150233 | 2 |
| C22×D1396 | 2 |
| #26013636 | 2 |
| #26013627 | 2 |
| #26013614 | 2 |
| #26013609 | 2 |
| #117×C349 | 2 |
| #535 | 349 |