Finite Group DatabasebetaFinite Group DatabasebetaOrder 5248.
456 conjugacy classes of subgroups; only the 264 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 264 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C41 | C24 |
| commutator | C22 | C23×C4×C41 |
| Frattini, cosocle | C23 | C24×C41 |
| prime radical | C24×C41 | C23 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C41×#389 | C2 | semidirect |
| 4. C41×#387 | C2 | semidirect |
| 6. C41×#384 | C2 | semidirect |
| 7. C41×#383 | C2 | semidirect |
| 9. #126×C41 | C4 | semidirect |
| 33. C4⋊C4×C41 | C2×C4 | semidirect |
| 37. C42×C41 | C2×C4 | semidirect |
| 68. #2383 | C41 | direct (N × H) |
| 74. #389 | C2×C41 | semidirect |
| 76. #387 | C2×C41 | semidirect |
| 78. #384 | C2×C41 | semidirect |
| 79. #383 | C2×C41 | semidirect |
| 80. C41 | #2383 | direct (N × H) |
| 82. #126 | C4×C41 | semidirect |
| 106. C4⋊C4 | C2×C4×C41 | semidirect |
| 110. C42 | C2×C4×C41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#126×C41 | 2 |
| C41×#389 | 2 |
| C41×#388 | 2 |
| C41×#387 | 2 |
| C41×#385 | 2 |
| C41×#384 | 2 |
| C41×#383 | 2 |
| #2383 | 41 |