Finite Group DatabasebetaFinite Group DatabasebetaOrder 5248.
908 conjugacy classes of subgroups; only the 360 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 360 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C41 | C23 |
| commutator, Frattini, cosocle | C23 | C24×C41 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C41×#395 | C2 | direct (N × H) |
| 21. C22×C4×C41 | Q8 | semidirect |
| 39. C2×C4×C41 | C2×Q8 | semidirect |
| 49. C2×#395 | C41 | direct (N × H) |
| 50. C2×C41 | #395 | direct (N × H) |
| 56. #395 | C2×C41 | direct (N × H) |
| 58. C41 | C2×#395 | direct (N × H) |
| 75. C22×C4 | Q8×C41 | semidirect |
| 93. C2×C4 | C2×Q8×C41 | semidirect |
| 103. C2 | C41×#395 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Q8×C41 | 2 |
| C22×C4⋊C4×C41 | 2 |
| C41×#395 | 2 |
| C2×#95×C41 | 2 |
| C2×#395 | 41 |