Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
234 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C59 | C2×D4 |
| commutator | C2×C4 | C22×C4×C59 |
| Frattini, cosocle | C42 | C23×C59 |
| socle | C22×C59 | C2×C22⋊C4 |
| prime radical | #121×C59 | C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C59 ◁ C2×C42×C59 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C4⋊C8×C59 | C2 | semidirect |
| 3. C4×M16×C59 | C2 | semidirect |
| 4. C59×Q8⋊C8 | C2 | semidirect |
| 5. C59×D4⋊C8 | C2 | semidirect |
| 89. #1483 | C59 | direct (N × H) |
| 96. C2×C4⋊C8 | C2×C59 | semidirect |
| 97. C4×M16 | C2×C59 | semidirect |
| 98. Q8⋊C8 | C2×C59 | semidirect |
| 99. D4⋊C8 | C2×C59 | semidirect |
| 100. C59 | #1483 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C59×#529 | 2 |
| C2×C4⋊C8×C59 | 2 |
| C4×M16×C59 | 2 |
| C59×Q8⋊C8 | 2 |
| C59×D4⋊C8 | 2 |
| #1483 | 59 |