Finite Group DatabasebetaFinite Group DatabasebetaOrder 5248.
214 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C41 | C2×C22⋊C4 |
| commutator | C23 | C22×C4×C41 |
| Frattini, cosocle | C22×C4 | C23×C41 |
| prime radical | C24×C41 | C2×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C41 ◁ C2×C42×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C41×#432 | C2 | semidirect |
| 3. C41×#431 | C2 | semidirect |
| 4. C41×#324 | C2 | semidirect |
| 87. #1473 | C41 | direct (N × H) |
| 94. #432 | C2×C41 | semidirect |
| 95. #431 | C2×C41 | semidirect |
| 96. #324 | C2×C41 | semidirect |
| 98. C41 | #1473 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#126×C41 | 2 |
| C41×#432 | 2 |
| C41×#431 | 2 |
| C41×#324 | 2 |
| C41×#323 | 2 |
| #1473 | 41 |