Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
406 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 116 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, Frattini, cosocle | C22×C4 | C23×C59 |
| prime radical | C22×D4×C59 | C22 |
| LCS | G ▷ C22×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⋊Q8×C59 | C2 | semidirect |
| 3. C2×#103×C59 | C2 | semidirect |
| 5. C59×#336 | C2 | semidirect |
| 60. C2×C4×C59 | SD16 | semidirect |
| 81. #2013 | C59 | direct (N × H) |
| 89. C2×C4⋊Q8 | C2×C59 | semidirect |
| 90. C2×#103 | C2×C59 | semidirect |
| 92. #336 | C2×C59 | semidirect |
| 93. C59 | #2013 | direct (N × H) |
| 148. C2×C4 | SD16×C59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×SD16×C59 | 2 |
| C2×C4⋊Q8×C59 | 2 |
| C2×#103×C59 | 2 |
| C59×#390 | 2 |
| C59×#336 | 2 |
| #2013 | 59 |