Finite Group DatabasebetaFinite Group DatabasebetaOrder 5248.
444 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 184 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C41 | D42 |
| commutator, Frattini, cosocle | C2×C4 | C24×C41 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C41 ◁ C2×C4×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C41×#578 | C2 | semidirect |
| 2. C41×#494 | C2 | semidirect |
| 3. C41×#473 | C2 | semidirect |
| 4. C41×#456 | C2 | semidirect |
| 5. C41×#443 | C2 | semidirect |
| 57. #3293 | C41 | direct (N × H) |
| 61. #578 | C2×C41 | semidirect |
| 62. #494 | C2×C41 | semidirect |
| 63. #473 | C2×C41 | semidirect |
| 64. #456 | C2×C41 | semidirect |
| 65. #443 | C2×C41 | semidirect |
| 66. C41 | #3293 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#578 | 2 |
| C41×#494 | 2 |
| C41×#473 | 2 |
| C41×#456 | 2 |
| C41×#443 | 2 |
| #3293 | 41 |