Finite Group DatabasebetaFinite Group DatabasebetaOrder 29312.
220 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 116 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C8×C229 | C2×D4 |
| commutator | C4 | C22×C8×C229 |
| Frattini, cosocle | C2×C8 | C23×C229 |
| socle | C2×C229 | C2×C22⋊C8 |
| prime radical | C2×#41×C229 | C4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C229 ◁ C22×C8×C229 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×M32×C229 | C2 | semidirect |
| 3. C2×M32×C229 | C2 | semidirect |
| 4. #350×C229 | C2 | semidirect |
| 17. M32×C229 | C22 | semidirect |
| 19. C2×C16×C229 | C22 | semidirect |
| 82. C229 | #2117 | direct (N × H) |
| 83. #2117 | C229 | direct (N × H) |
| 85. C2×M32 | C2×C229 | semidirect |
| 86. C2×M32 | C2×C229 | semidirect |
| 87. #350 | C2×C229 | semidirect |
| 100. M32 | C22×C229 | semidirect |
| 102. C2×C16 | C22×C229 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#131×C229 | 2 |
| C2×M32×C229 | 2 |
| #350×C229 | 2 |
| #2117 | 229 |