Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
456 conjugacy classes of subgroups; only the 264 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 264 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C227 | C24 |
| commutator | C22 | C23×C4×C227 |
| Frattini, cosocle | C23 | C24×C227 |
| prime radical | C24×C227 | C23 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C227 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #389×C227 | C2 | semidirect |
| 4. #387×C227 | C2 | semidirect |
| 6. #384×C227 | C2 | semidirect |
| 7. #383×C227 | C2 | semidirect |
| 9. #126×C227 | C4 | semidirect |
| 33. C4⋊C4×C227 | C2×C4 | semidirect |
| 37. C42×C227 | C2×C4 | semidirect |
| 72. C227 | #2383 | direct (N × H) |
| 73. #2383 | C227 | direct (N × H) |
| 75. #389 | C2×C227 | semidirect |
| 77. #387 | C2×C227 | semidirect |
| 79. #384 | C2×C227 | semidirect |
| 80. #383 | C2×C227 | semidirect |
| 82. #126 | C4×C227 | semidirect |
| 106. C4⋊C4 | C2×C4×C227 | semidirect |
| 110. C42 | C2×C4×C227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#126×C227 | 2 |
| #389×C227 | 2 |
| #388×C227 | 2 |
| #387×C227 | 2 |
| #385×C227 | 2 |
| #384×C227 | 2 |
| #383×C227 | 2 |
| #2383 | 227 |