Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
204 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C199 | #397 |
| commutator, Frattini, cosocle | C22×C4 | C23×C199 |
| prime radical | C22×D4×C199 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C199 ◁ C22×C4×C199 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #430×C199 | C2 | semidirect |
| 5. #344×C199 | C2 | semidirect |
| 6. #344×C199 | C2 | semidirect |
| 7. H(3,ℤ/4)×C199 | C2 | semidirect |
| 85. C199 | #2081 | direct (N × H) |
| 86. #2081 | C199 | direct (N × H) |
| 87. #430 | C2×C199 | semidirect |
| 91. #344 | C2×C199 | semidirect |
| 92. #344 | C2×C199 | semidirect |
| 93. H(3,ℤ/4) | C2×C199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #430×C199 | 2 |
| #418×C199 | 2 |
| C2×#100×C199 | 2 |
| #344×C199 | 2 |
| H(3,ℤ/4)×C199 | 2 |
| #2081 | 199 |