Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
4638 conjugacy classes of subgroups; only the 3000 normal subgroups are shown.
This group has 4638 conjugacy classes of subgroups — too many to draw. Only its 3000 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 | C23×C4×C8 |
| Frattini | C22 | C24×#595 |
| Fitting | C24×C4×C17 | C4 |
| socle, prime radical | C25×C17 | C2×C4 |
| cosocle | C2×Dic17 | C25 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C24×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×C4×#3624 | C2 | direct (N × H) |
| 4. C23×#3624 | C4 | direct (N × H) |
| 6. C2×C4×#3624 | C22 | direct (N × H) |
| 13. C23×C4×C17 | C8 | semidirect |
| 15. C23×Dic17 | C8 | semidirect |
| 20. C22×#3624 | C2×C4 | direct (N × H) |
| 24. C4×#3624 | C23 | direct (N × H) |
| 29. C22×C4×C17 | C2×C8 | semidirect |
| 32. C22×Dic17 | C2×C8 | semidirect |
| 37. C2×#3624 | C22×C4 | direct (N × H) |
| 42. C23×C17 | C4×C8 | semidirect |
| 47. C2×C4×C17 | C22×C8 | semidirect |
| 50. C2×Dic17 | C22×C8 | semidirect |
| 55. #3624 | C23×C4 | direct (N × H) |
| 59. C22×C17 | C2×C4×C8 | semidirect |
| 64. C4×C17 | C23×C8 | semidirect |
| 66. Dic17 | C23×C8 | semidirect |
| 76. C2×C17 | C22×C4×C8 | semidirect |
| 86. C23×C4 | #3624 | direct (N × H) |
| 93. C17 | C23×C4×C8 | semidirect |
| 104. C22×C4 | C2×#3624 | direct (N × H) |
| 110. C23 | C4×#3624 | direct (N × H) |
| 121. C2×C4 | C22×#3624 | direct (N × H) |
| 124. C22 | C2×C4×#3624 | direct (N × H) |
| 132. C4 | C23×#3624 | direct (N × H) |
| 133. C2 | C22×C4×#3624 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×#3624 | 2 |
| C22×C4×#3624 | 2 |
| C23×C4×Dic17 | 2 |
| C23×C4×C8 | 17 |