Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
274 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 80 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×C59 | #394 |
| commutator, Frattini, cosocle | C22×C4 | C23×C59 |
| prime radical | C2×AGL(1,ℤ/8)×C59 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C59 ◁ C22×C4×C59 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C59×#430 | C2 | semidirect |
| 3. C59×#421 | C2 | semidirect |
| 4. C59×#418 | C2 | semidirect |
| 5. C59×#413 | C2 | semidirect |
| 6. C2×#100×C59 | C2 | semidirect |
| 7. C59×#344 | C2 | semidirect |
| 104. #2048 | C59 | direct (N × H) |
| 112. #430 | C2×C59 | semidirect |
| 113. #421 | C2×C59 | semidirect |
| 114. #418 | C2×C59 | semidirect |
| 115. #413 | C2×C59 | semidirect |
| 116. C2×#100 | C2×C59 | semidirect |
| 117. #344 | C2×C59 | semidirect |
| 118. C59 | #2048 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×AGL(1,ℤ/8)×C59 | 2 |
| C59×#430 | 2 |
| C59×#421 | 2 |
| C59×#418 | 2 |
| C59×#413 | 2 |
| C2×#100×C59 | 2 |
| C59×#344 | 2 |
| #2048 | 59 |