Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
256 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 72 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×C59 | #120 |
| commutator, Frattini, cosocle | C42 | C23×C59 |
| prime radical | C59×#550 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C42×C59 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C59×#492 | C2 | semidirect |
| 3. C59×#477 | C2 | semidirect |
| 4. C59×#476 | C2 | semidirect |
| 5. C59×#331 | C2 | semidirect |
| 6. C59×Q8⋊C8 | C2 | semidirect |
| 7. C59×D4⋊C8 | C2 | semidirect |
| 54. Q8×C59 | SD16 | semidirect |
| 93. #1631 | C59 | direct (N × H) |
| 100. #492 | C2×C59 | semidirect |
| 101. #477 | C2×C59 | semidirect |
| 102. #476 | C2×C59 | semidirect |
| 103. #331 | C2×C59 | semidirect |
| 104. Q8⋊C8 | C2×C59 | semidirect |
| 105. D4⋊C8 | C2×C59 | semidirect |
| 106. C59 | #1631 | direct (N × H) |
| 153. Q8 | SD16×C59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C59×#550 | 2 |
| C59×#492 | 2 |
| C59×#477 | 2 |
| C59×#476 | 2 |
| C59×#331 | 2 |
| C59×Q8⋊C8 | 2 |
| C59×D4⋊C8 | 2 |
| #1631 | 59 |