Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
820 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 144 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 | C2×C22⋊C4 |
| commutator | C23 | C22×C4×C59 |
| Frattini, cosocle | C22×C4 | C23×C59 |
| prime radical | C23×D4×C59 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C23×C4×C59 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#100×C59 | C2 | semidirect |
| 3. C59×#407 | C2 | semidirect |
| 10. C2×M16×C59 | C22 | semidirect |
| 59. C22×C59 | #100 | semidirect |
| 64. #1783 | C59 | direct (N × H) |
| 71. C2×#100 | C2×C59 | semidirect |
| 72. #407 | C2×C59 | semidirect |
| 73. C59 | #1783 | direct (N × H) |
| 80. C2×M16 | C22×C59 | semidirect |
| 129. C22 | #100×C59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D4×C59 | 2 |
| C2×#100×C59 | 2 |
| C59×#407 | 2 |
| #1783 | 59 |