Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
356 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 136 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C59 | C2×D4 |
| commutator | C2×C4 | C22×C4×C59 |
| Frattini, cosocle | C22×C4 | C23×C59 |
| prime radical | C22×D4×C59 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×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 |
| 4. C59×#382 | C2 | semidirect |
| 5. C59×#340 | C2 | semidirect |
| 10. C4×D4×C59 | C4 | semidirect |
| 88. #1804 | C59 | direct (N × H) |
| 96. C2×C4⋊C8 | C2×C59 | semidirect |
| 98. #382 | C2×C59 | semidirect |
| 99. #340 | C2×C59 | semidirect |
| 100. C59 | #1804 | direct (N × H) |
| 105. C4×D4 | C4×C59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D4×C59 | 2 |
| C2×C4⋊C8×C59 | 2 |
| C2×#102×C59 | 2 |
| C59×#382 | 2 |
| C59×#340 | 2 |
| #1804 | 59 |