Finite Group DatabasebetaFinite Group DatabasebetaOrder 5248.
816 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 232 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, Frattini, cosocle | C23 | C24×C41 |
| prime radical | C22×#41×C41 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C22⋊Q8×C41 | C2 | semidirect |
| 3. C41×#395 | C2 | semidirect |
| 4. C41×#394 | C2 | semidirect |
| 5. C41×#380 | C2 | semidirect |
| 62. #2616 | C41 | direct (N × H) |
| 68. C2×C22⋊Q8 | C2×C41 | semidirect |
| 69. #395 | C2×C41 | semidirect |
| 70. #394 | C2×C41 | semidirect |
| 71. #380 | C2×C41 | semidirect |
| 72. C41 | #2616 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#41×C41 | 2 |
| C2×C22⋊Q8×C41 | 2 |
| C41×#395 | 2 |
| C41×#394 | 2 |
| C41×#380 | 2 |
| #2616 | 41 |