Finite Group DatabasebetaFinite Group DatabasebetaOrder 29824.
324 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 136 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C233 | C23 |
| commutator | C23 | C22×C4×C233 |
| Frattini, cosocle | C22×C4 | C23×C233 |
| socle | C23×C233 | C22×C4 |
| prime radical | C24×C233 | C2×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C233 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C4⋊C8×C233 | C2 | semidirect |
| 5. #336×C233 | C2 | semidirect |
| 54. C2×C4×C233 | M16 | semidirect |
| 84. C233 | #1851 | direct (N × H) |
| 85. #1851 | C233 | direct (N × H) |
| 87. C2×C4⋊C8 | C2×C233 | semidirect |
| 90. #336 | C2×C233 | semidirect |
| 139. C2×C4 | M16×C233 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×M16×C233 | 2 |
| C2×C4⋊C8×C233 | 2 |
| C2×C22⋊C8×C233 | 2 |
| C4×C22⋊C4×C233 | 2 |
| #336×C233 | 2 |
| #1851 | 233 |