Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
930 conjugacy classes of subgroups; only the 760 normal subgroups are shown.
This group has 930 conjugacy classes of subgroups — too many to draw. Only its 760 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C227 | C24 |
| commutator, Frattini, cosocle | C22 | C25×C227 |
| socle | C22×C227 | C25 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C227 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #564×C227 | C2 | semidirect |
| 2. #563×C227 | C2 | semidirect |
| 3. #562×C227 | C2 | semidirect |
| 4. #533×C227 | C2 | semidirect |
| 5. #529×C227 | C2 | semidirect |
| 53. C227 | #3531 | direct (N × H) |
| 54. #3531 | C227 | direct (N × H) |
| 55. #564 | C2×C227 | semidirect |
| 56. #563 | C2×C227 | semidirect |
| 57. #562 | C2×C227 | semidirect |
| 58. #533 | C2×C227 | semidirect |
| 59. #529 | C2×C227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #564×C227 | 2 |
| #563×C227 | 2 |
| #562×C227 | 2 |
| #533×C227 | 2 |
| #529×C227 | 2 |
| #3531 | 227 |