Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
334 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 112 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 | C2×C4 | C22×C4×C59 |
| Frattini, cosocle | C22×C4 | C23×C59 |
| prime radical | C2×#41×C59 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C22×C4×C59 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C59×#419 | C2 | semidirect |
| 5. C59×#391 | C2 | semidirect |
| 6. C59×#343 | C2 | semidirect |
| 7. C59×#339 | C2 | semidirect |
| 11. #137×C59 | C4 | semidirect |
| 37. C2×Q8×C59 | C2×C4 | semidirect |
| 52. M16×C59 | C2×C4 | semidirect |
| 118. #1882 | C59 | direct (N × H) |
| 128. #419 | C2×C59 | semidirect |
| 129. #391 | C2×C59 | semidirect |
| 130. #343 | C2×C59 | semidirect |
| 131. #339 | C2×C59 | semidirect |
| 132. C59 | #1882 | direct (N × H) |
| 136. #137 | C4×C59 | semidirect |
| 162. C2×Q8 | C2×C4×C59 | semidirect |
| 177. M16 | C2×C4×C59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#137×C59 | 2 |
| C59×#520 | 2 |
| C2×#104×C59 | 2 |
| C59×#419 | 2 |
| C59×#391 | 2 |
| C59×#343 | 2 |
| C59×#339 | 2 |
| #1882 | 59 |