Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
216 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C16×C29 | D8 |
| commutator | C8 | C22×C8×C29 |
| Frattini, cosocle | C4×C8 | C23×C29 |
| socle | C2×C29 | C8×D8 |
| prime radical | C29×#508 | C4 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C16×C29 ◁ C2×C16×C29 ◁ C4×C16×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×#2170 | C2 | semidirect |
| 3. C29×#1373 | C2 | semidirect |
| 4. C29×#1335 | C2 | semidirect |
| 5. C8×C16×C29 | C2 | semidirect |
| 18. C29×Q32 | C8 | semidirect |
| 19. C29×SD32 | C8 | semidirect |
| 20. C29×D16 | C8 | semidirect |
| 50. #12046 | C29 | direct (N × H) |
| 64. #2170 | C2×C29 | semidirect |
| 65. #1373 | C2×C29 | semidirect |
| 66. #1335 | C2×C29 | semidirect |
| 67. C8×C16 | C2×C29 | semidirect |
| 89. Q32 | C8×C29 | semidirect |
| 90. SD32 | C8×C29 | semidirect |
| 91. D16 | C8×C29 | semidirect |
| 103. C29 | #12046 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#2178 | 2 |
| C29×#2170 | 2 |
| C29×#1373 | 2 |
| C29×#1335 | 2 |
| C8×C16×C29 | 2 |
| #12046 | 29 |