Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
288 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C29 | #2184 |
| commutator, Frattini, cosocle | C2×C16 | C23×C29 |
| LCS | G ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C29 ◁ C2×C4×C29 ◁ C29×#131 ◁ C29×#504 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C29×#3415 | C2 | semidirect |
| 2. C29×#2263 | C2 | semidirect |
| 3. C2×C29×D32 | C2 | semidirect |
| 4. C29×#2221 | C2 | semidirect |
| 5. C29×#1419 | C2 | semidirect |
| 6. C29×#1417 | C2 | semidirect |
| 7. C29×#1401 | C2 | semidirect |
| 15. C2×C29×D16 | C22 | semidirect |
| 21. C29×M64 | C22 | semidirect |
| 22. C2×C29×C32 | C22 | semidirect |
| 23. C29×#368 | C22 | semidirect |
| 80. #13669 | C29 | direct (N × H) |
| 104. #3415 | C2×C29 | semidirect |
| 105. #2263 | C2×C29 | semidirect |
| 106. C2×D32 | C2×C29 | semidirect |
| 107. #2221 | C2×C29 | semidirect |
| 108. #1419 | C2×C29 | semidirect |
| 109. #1417 | C2×C29 | semidirect |
| 110. #1401 | C2×C29 | semidirect |
| 130. C2×D16 | C22×C29 | semidirect |
| 136. M64 | C22×C29 | semidirect |
| 137. C2×C32 | C22×C29 | semidirect |
| 138. #368 | C22×C29 | semidirect |
| 173. C29 | #13669 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#3415 | 2 |
| C29×#2263 | 2 |
| C2×C29×D32 | 2 |
| C29×#2221 | 2 |
| C29×#1419 | 2 |
| C29×#1417 | 2 |
| C29×#1401 | 2 |
| #13669 | 29 |