Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
6640 conjugacy classes of subgroups; only the 5670 normal subgroups are shown.
This group has 6640 conjugacy classes of subgroups — too many to draw. Only its 5670 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C42×C29 | C24 |
| commutator, Frattini, cosocle | C22 | C26×C29 |
| socle | C22×C29 | C26 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C42×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C29×#3531 | C2 | semidirect |
| 2. C29×#3529 | C2 | semidirect |
| 3. C29×#3444 | C2 | semidirect |
| 4. C29×#564 | C22 | semidirect |
| 5. C29×#563 | C22 | semidirect |
| 6. C29×#562 | C22 | semidirect |
| 7. C29×H(3,𝔽4) | C22 | semidirect |
| 8. C29×#560 | C22 | semidirect |
| 9. C29×#533 | C22 | semidirect |
| 11. C29×#529 | C22 | semidirect |
| 12. C29×#525 | C22 | semidirect |
| 13. C4×#41×C29 | C22 | semidirect |
| 14. C22×C42×C29 | C22 | semidirect |
| 44. #62694 | C29 | direct (N × H) |
| 53. #3531 | C2×C29 | semidirect |
| 54. #3529 | C2×C29 | semidirect |
| 55. #3444 | C2×C29 | semidirect |
| 61. #564 | C22×C29 | semidirect |
| 62. #563 | C22×C29 | semidirect |
| 63. #562 | C22×C29 | semidirect |
| 64. H(3,𝔽4) | C22×C29 | semidirect |
| 65. #560 | C22×C29 | semidirect |
| 66. #533 | C22×C29 | semidirect |
| 68. #529 | C22×C29 | semidirect |
| 69. #525 | C22×C29 | semidirect |
| 70. C4×#41 | C22×C29 | semidirect |
| 71. C22×C42 | C22×C29 | semidirect |
| 90. C29 | #62694 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#3531 | 2 |
| C29×#3529 | 2 |
| C29×#3444 | 2 |
| #62694 | 29 |