Finite Group DatabasebetaFinite Group DatabasebetaOrder 38220.
104 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | #19129729 |
| commutator, hypocenter | C5×C7×C13 | C3×C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C5×C72×C13 | C3×C4 |
| prime radical | C7×D5×#63270 | C2 |
| cosocle | C7×D5×C13 | C2×C3×C7 |
| LCS | G ▷ C5×C7×C13 | |
| UCS | C1 ◁ C7 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C7×C7⋊#63120 | C3 | semidirect |
| 3. C5×C7×#63270 | C4 | semidirect |
| 6. #19129729 | C7 | direct (N × H) |
| 9. C5×C72×C13 | C3×C4 | semidirect |
| 14. C7×#63270 | AGL(1,𝔽5) | semidirect |
| 15. C7⋊#63120 | C3×C7 | semidirect |
| 18. C5×#63270 | C4×C7 | semidirect |
| 29. C72×C13 | C3×AGL(1,𝔽5) | semidirect |
| 35. C5×C7×C13 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 36. C5×C7×C13 | C3×C4×C7 | semidirect |
| 43. #63270 | C7×AGL(1,𝔽5) | semidirect |
| 46. C5×C72 | Dic13⋊C3 | semidirect |
| 63. C7×C13 | ΓL(1,𝔽8)⋊AGL(1,𝔽5) | semidirect |
| 64. C7×C13 | C3×C7×AGL(1,𝔽5) | semidirect |
| 71. C5×C13 | C7×ΓL(1,𝔽8)⋊C4 | semidirect |
| 74. C72 | #63120⋊C3 | semidirect |
| 79. C5×C7 | C7×Dic13⋊C3 | semidirect |
| 80. C5×C7 | #11763963 | semidirect |
| 92. C13 | C7×ΓL(1,𝔽8)⋊AGL(1,𝔽5) | semidirect |
| 96. C7 | C7×#63120⋊C3 | semidirect |
| 97. C7 | #19129729 | direct (N × H) |
| 99. C5 | C7×#11763963 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×D5×#63270 | 2 |
| C7×C7⋊#63120 | 3 |
| C7×#11763963 | 5 |
| #19129729 | 7 |
| C7×#63120⋊C3 | 7 |
| C7×ΓL(1,𝔽8)⋊AGL(1,𝔽5) | 13 |