Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
230 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 230 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 |
| 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×#135×C227 | C2 | semidirect |
| 2. C2×SD32×C227 | C2 | semidirect |
| 3. C2×D16×C227 | C2 | semidirect |
| 4. #466×C227 | C2 | semidirect |
| 5. #358×C227 | C2 | semidirect |
| 6. #357×C227 | C2 | semidirect |
| 7. C22⋊C16×C227 | C2 | semidirect |
| 33. Q16×C227 | D4 | semidirect |
| 38. D8×C227 | D4 | semidirect |
| 89. C227 | #2186 | direct (N × H) |
| 90. #2186 | C227 | direct (N × H) |
| 91. C2×#135 | C2×C227 | semidirect |
| 92. C2×SD32 | C2×C227 | semidirect |
| 93. C2×D16 | C2×C227 | semidirect |
| 94. #466 | C2×C227 | semidirect |
| 95. #358 | C2×C227 | semidirect |
| 96. #357 | C2×C227 | semidirect |
| 97. C22⋊C16 | C2×C227 | semidirect |
| 123. Q16 | D4×C227 | semidirect |
| 128. D8 | D4×C227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#135×C227 | 2 |
| C2×SD32×C227 | 2 |
| C2×D16×C227 | 2 |
| #466×C227 | 2 |
| #358×C227 | 2 |
| #357×C227 | 2 |
| C22⋊C16×C227 | 2 |
| #2186 | 227 |