Finite Group DatabasebetaFinite Group DatabasebetaOrder 22592.
228 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 113 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 | C4×D4×C353 | C2 |
| prime radical | C2×D4×C353 | C22 |
| hypercenter | C4×D4 | D353 |
| hypocenter | C353 | #554 |
| LCS | G ▷ C22×C353 ▷ C353 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #26014991 | C2 | semidirect |
| 2. #26014984 | C2 | semidirect |
| 3. #26014983 | C2 | semidirect |
| 4. #26014971 | C2 | semidirect |
| 5. #26014969 | C2 | semidirect |
| 6. #26014969 | C2 | semidirect |
| 7. C4×Dic706 | C2 | semidirect |
| 10. C2×#19150716 | C2 | semidirect |
| 46. D4×C353 | Q8 | semidirect |
| 70. C353 | #554 | semidirect |
| 109. D4 | Dic706 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26014991 | 2 |
| #26014984 | 2 |
| #26014983 | 2 |
| #26014971 | 2 |
| #26014969 | 2 |
| C4×Dic706 | 2 |
| D4×Dic353 | 2 |
| C2×#19150716 | 2 |
| C4×D4×C353 | 2 |
| #554 | 353 |