Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
1068 conjugacy classes of subgroups; only the 288 normal subgroups are shown.
This group has 1068 conjugacy classes of subgroups — too many to draw. Only its 288 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 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C59 |
| prime radical | C25×C59 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C59 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C22⋊Q8×C59 | C2 | semidirect |
| 3. C59×#385 | C2 | semidirect |
| 4. C59×#380 | C2 | semidirect |
| 7. C22×Q8×C59 | C22 | semidirect |
| 12. C2×C4⋊C4×C59 | C22 | semidirect |
| 13. C2×C4⋊C4×C59 | C22 | semidirect |
| 16. #95×C59 | C22 | semidirect |
| 19. C24×C59 | Q8 | semidirect |
| 58. C22×C59 | C22⋊Q8 | semidirect |
| 66. #2848 | C59 | direct (N × H) |
| 72. C2×C22⋊Q8 | C2×C59 | semidirect |
| 73. #385 | C2×C59 | semidirect |
| 74. #380 | C2×C59 | semidirect |
| 76. C59 | #2848 | direct (N × H) |
| 78. C22×Q8 | C22×C59 | semidirect |
| 83. C2×C4⋊C4 | C22×C59 | semidirect |
| 84. C2×C4⋊C4 | C22×C59 | semidirect |
| 87. #95 | C22×C59 | semidirect |
| 90. C24 | Q8×C59 | semidirect |
| 129. C22 | C22⋊Q8×C59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C4×C59 | 2 |
| C2×C22⋊Q8×C59 | 2 |
| C59×#385 | 2 |
| C59×#380 | 2 |
| C59×#379 | 2 |
| #2848 | 59 |