Finite Group DatabasebetaFinite Group DatabasebetaOrder 4704.
650 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×#64425 |
| commutator, socle, cosocle | C22×C72 | C23×C3 |
| Fitting | C24×C72 | C2×C3 |
| hypercenter | C24 | #64425 |
| hypocenter | C72 | C3×#120 |
| LCS | G ▷ C22×C72 ▷ C72 | |
| UCS | C1 ◁ C22 ◁ C24 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72246062 | C2 | semidirect |
| 2. C24×#3862 | C2 | semidirect |
| 3. C2×#11924222 | C2 | semidirect |
| 4. #13096593 | C3 | semidirect |
| 7. C22×#64425 | C22 | semidirect |
| 9. C2×#10596875 | C22 | semidirect |
| 10. C24×C72 | C2×C3 | semidirect |
| 11. C2×C22⋊(C7⋊D7) | C2×C3 | semidirect |
| 12. C22⋊(C7⋊Dic7) | C2×C3 | semidirect |
| 17. C22×#3862 | D4 | semidirect |
| 23. C22×C7⋊D7 | C22×C3 | semidirect |
| 25. C2×C7⋊Dic7 | C22×C3 | semidirect |
| 40. C22×C72 | C3×D4 | semidirect |
| 54. #3862 | #120 | semidirect |
| 56. C24×C7 | AGL(1,𝔽7) | semidirect |
| 57. C24×C7 | AGL(1,𝔽7) | semidirect |
| 95. C72 | C3×#120 | semidirect |
| 114. C22×C7 | (C22⋊D7)⋊C3 | semidirect |
| 115. C22×C7 | (C22⋊D7)⋊C3 | semidirect |
| 131. C24 | #64425 | semidirect |
| 155. C7 | #10620789 | semidirect |
| 156. C7 | #10620789 | semidirect |
| 163. C22 | #11924222 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72246062 | 2 |
| C24×#3862 | 2 |
| C2×#11924222 | 2 |
| #13096593 | 3 |
| #10620789 | 7 |