Finite Group DatabasebetaFinite Group DatabasebetaOrder 5248.
174 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 68 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×D8 |
| commutator, Frattini, cosocle | C2×C8 | C23×C41 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C41 ◁ C22×C4×C41 ◁ C22×C8×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×D16×C41 | C2 | semidirect |
| 2. C22×C16×C41 | C2 | semidirect |
| 3. C41×#466 | C2 | semidirect |
| 4. C41×#366 | C2 | semidirect |
| 5. C41×#357 | C2 | semidirect |
| 27. C16×C41 | D4 | semidirect |
| 46. C22×C41 | D16 | semidirect |
| 52. #2215 | C41 | direct (N × H) |
| 58. C2×D16 | C2×C41 | semidirect |
| 59. C22×C16 | C2×C41 | semidirect |
| 60. #466 | C2×C41 | semidirect |
| 61. #366 | C2×C41 | semidirect |
| 62. #357 | C2×C41 | semidirect |
| 63. C41 | #2215 | direct (N × H) |
| 85. C16 | D4×C41 | semidirect |
| 104. C22 | D16×C41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D16×C41 | 2 |
| C22×C16×C41 | 2 |
| C41×#466 | 2 |
| C41×#366 | 2 |
| C41×#357 | 2 |
| #2215 | 41 |