Finite Group DatabasebetaFinite Group DatabasebetaOrder 22592.
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×D353 |
| commutator, socle, cosocle | C22×C353 | C24 |
| Fitting | C2×#41×C353 | C2 |
| hypercenter | C2×#41 | D353 |
| hypocenter | C353 | #535 |
| LCS | G ▷ C22×C353 ▷ C353 | |
| UCS | C1 ◁ C22 ◁ C2×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×D1412 | C2 | semidirect |
| 2. #26014988 | C2 | semidirect |
| 3. #26014981 | C2 | semidirect |
| 4. #26014966 | C2 | semidirect |
| 5. #26014960 | C2 | semidirect |
| 6. #26014951 | C2 | semidirect |
| 7. C2×#41×C353 | C2 | semidirect |
| 12. C2×C22⋊D353 | C22 | semidirect |
| 13. C4⋊Dic353 | C22 | semidirect |
| 15. #19150714 | C22 | semidirect |
| 16. C4×Dic353 | C22 | semidirect |
| 18. C2×Q8×C353 | C22 | semidirect |
| 20. C2×D4×C353 | C22 | semidirect |
| 22. C22×C4×C353 | C22 | semidirect |
| 36. C2×C4×C353 | D4 | semidirect |
| 57. C353 | #535 | semidirect |
| 59. C2×#41 | D353 | semidirect |
| 68. C2×Q8 | C2×D353 | semidirect |
| 74. C2×D4 | C2×D353 | semidirect |
| 76. C22×C4 | C2×D353 | semidirect |
| 94. C2×C4 | C22⋊D353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1412 | 2 |
| #26014988 | 2 |
| #26014981 | 2 |
| #26014966 | 2 |
| #26014960 | 2 |
| #26014951 | 2 |
| C2×#41×C353 | 2 |
| #535 | 353 |