Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
208 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 60 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 | #120 |
| commutator, Frattini, cosocle | C42 | C23×C59 |
| prime radical | C59×#562 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C42×C59 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C59×#501 | C2 | semidirect |
| 3. C59×#497 | C2 | semidirect |
| 4. C59×#489 | C2 | semidirect |
| 5. C59×#330 | C2 | semidirect |
| 6. C59×#329 | C2 | semidirect |
| 7. C59×#329 | C2 | semidirect |
| 94. #1661 | C59 | direct (N × H) |
| 101. #501 | C2×C59 | semidirect |
| 102. #497 | C2×C59 | semidirect |
| 103. #489 | C2×C59 | semidirect |
| 104. #330 | C2×C59 | semidirect |
| 105. #329 | C2×C59 | semidirect |
| 106. #329 | C2×C59 | semidirect |
| 107. C59 | #1661 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C59×#562 | 2 |
| C59×#501 | 2 |
| C59×#497 | 2 |
| C59×#489 | 2 |
| C59×#330 | 2 |
| C59×#329 | 2 |
| #1661 | 59 |