Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
770 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 770 conjugacy classes of subgroups — too many to draw. Only its 102 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×C29 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C29 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C29×#3213 | C2 | semidirect |
| 2. C29×#3151 | C2 | semidirect |
| 3. C29×#2657 | C2 | semidirect |
| 4. C29×#1555 | C2 | semidirect |
| 5. C29×#1527 | C2 | semidirect |
| 6. C29×#1505 | C2 | semidirect |
| 7. C29×#1300 | C2 | semidirect |
| 44. C29×C4⋊Q8 | D4 | semidirect |
| 50. C29×#127 | D4 | semidirect |
| 67. C29×C4⋊C8 | D4 | semidirect |
| 74. C29×#97 | D4 | semidirect |
| 133. #10088 | C29 | direct (N × H) |
| 180. #3213 | C2×C29 | semidirect |
| 181. #3151 | C2×C29 | semidirect |
| 182. #2657 | C2×C29 | semidirect |
| 183. #1555 | C2×C29 | semidirect |
| 184. #1527 | C2×C29 | semidirect |
| 185. #1505 | C2×C29 | semidirect |
| 186. #1300 | C2×C29 | semidirect |
| 255. C4⋊Q8 | D4×C29 | semidirect |
| 261. #127 | D4×C29 | semidirect |
| 278. C4⋊C8 | D4×C29 | semidirect |
| 285. #97 | D4×C29 | semidirect |
| 289. C29 | #10088 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#3213 | 2 |
| C29×#3151 | 2 |
| C29×#2657 | 2 |
| C29×#1555 | 2 |
| C29×#1527 | 2 |
| C29×#1505 | 2 |
| C29×#1300 | 2 |
| #10088 | 29 |