Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
164 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 68 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×C227 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C23×C227 |
| prime radical | #466×C227 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C227 ◁ C22×C4×C227 ◁ C22×C8×C227 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×SD32×C227 | C2 | semidirect |
| 2. C22×C16×C227 | C2 | semidirect |
| 3. #467×C227 | C2 | semidirect |
| 5. #367×C227 | C2 | semidirect |
| 6. #358×C227 | C2 | semidirect |
| 7. #357×C227 | C2 | semidirect |
| 39. C16×C227 | D4 | semidirect |
| 62. C22×C227 | SD32 | semidirect |
| 75. C227 | #2217 | direct (N × H) |
| 76. #2217 | C227 | direct (N × H) |
| 77. C2×SD32 | C2×C227 | semidirect |
| 78. C22×C16 | C2×C227 | semidirect |
| 79. #467 | C2×C227 | semidirect |
| 81. #367 | C2×C227 | semidirect |
| 82. #358 | C2×C227 | semidirect |
| 83. #357 | C2×C227 | semidirect |
| 115. C16 | D4×C227 | semidirect |
| 138. C22 | SD32×C227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×SD32×C227 | 2 |
| C22×C16×C227 | 2 |
| #467×C227 | 2 |
| #466×C227 | 2 |
| #367×C227 | 2 |
| #358×C227 | 2 |
| #357×C227 | 2 |
| #2217 | 227 |