Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
160 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 92 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×C199 | C22⋊C4 |
| commutator | C22 | C4×C8×C199 |
| Frattini, cosocle | C2×C42 | C22×C199 |
| socle | C22×C199 | #95 |
| prime radical | C23×C199 | C42 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C199 ◁ C2×C42×C199 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 18. M16×C199 | C8 | semidirect |
| 59. C199 | #1283 | direct (N × H) |
| 60. #1283 | C199 | direct (N × H) |
| 78. M16 | C8×C199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #431×C199 | 2 |
| C2×C4⋊C8×C199 | 2 |
| C4×M16×C199 | 2 |
| #1283 | 199 |