Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
712 conjugacy classes of subgroups; only the 440 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 440 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C59 | C23 |
| commutator | C22 | C23×C4×C59 |
| Frattini, cosocle | C23 | C24×C59 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C59 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C59×#382 | C2 | direct (N × H) |
| 10. C2×C42×C59 | C4 | semidirect |
| 25. C42×C59 | C2×C4 | semidirect |
| 52. C2×#382 | C59 | direct (N × H) |
| 53. C2×C59 | #382 | direct (N × H) |
| 60. #382 | C2×C59 | direct (N × H) |
| 62. C59 | C2×#382 | direct (N × H) |
| 68. C2×C42 | C4×C59 | semidirect |
| 83. C42 | C2×C4×C59 | semidirect |
| 110. C2 | C59×#382 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊C4×C59 | 2 |
| C22×C42×C59 | 2 |
| C59×#382 | 2 |
| C2×#95×C59 | 2 |
| C2×#382 | 59 |