Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
15454 conjugacy classes of subgroups; only the 8408 normal subgroups are shown.
This group has 15454 conjugacy classes of subgroups — too many to draw. Only its 8408 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24×C4 | #595 |
| commutator, hypocenter | C17 | C25×C8 |
| Frattini | C2 | C25×#595 |
| Fitting | C24×C4×C17 | C4 |
| socle | C25×C17 | C2×C4 |
| prime radical | C25×D17 | C4 |
| cosocle | Dic17 | C26 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C24×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×#63242 | C2 | direct (N × H) |
| 2. C24×#3624 | C2 | semidirect |
| 4. C22×#63242 | C22 | direct (N × H) |
| 5. C23×#3624 | C22 | semidirect |
| 12. C24×D17 | C8 | semidirect |
| 19. C22×#3624 | C23 | semidirect |
| 20. C2×#63242 | C23 | direct (N × H) |
| 21. C24×C17 | C2×C8 | semidirect |
| 23. C23×D17 | C2×C8 | semidirect |
| 30. C2×#3624 | C24 | semidirect |
| 31. #63242 | C24 | direct (N × H) |
| 33. C23×C17 | C22×C8 | semidirect |
| 35. C22×D17 | C22×C8 | semidirect |
| 42. #3624 | C25 | semidirect |
| 46. C22×C17 | C23×C8 | semidirect |
| 48. C2×D17 | C23×C8 | semidirect |
| 60. C2×C17 | C24×C8 | semidirect |
| 62. D17 | C24×C8 | semidirect |
| 73. C17 | C25×C8 | semidirect |
| 76. C24 | #63242 | direct (N × H) |
| 87. C23 | C2×#63242 | direct (N × H) |
| 97. C22 | C22×#63242 | direct (N × H) |
| 103. C2 | C23×#63242 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#63242 | 2 |
| C24×#3624 | 2 |
| C24×C4×D17 | 2 |
| C25×C8 | 17 |