Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
208 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C199 | #121 |
| commutator, Frattini, cosocle | C22×C4 | C23×C199 |
| prime radical | C23×C199 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C199 ◁ C22×C4×C199 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 90. C199 | #2064 | direct (N × H) |
| 91. #2064 | C199 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#108×C199 | 2 |
| #428×C199 | 2 |
| #424×C199 | 2 |
| #419×C199 | 2 |
| C2×#103×C199 | 2 |
| C2×#101×C199 | 2 |
| #343×C199 | 2 |
| #2064 | 199 |