Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
212 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 108 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×C197 | C22⋊C4 |
| commutator | C2×C4 | C22×C4×C197 |
| Frattini, cosocle | C42 | C23×C197 |
| socle | C22×C197 | C2×C22⋊C4 |
| prime radical | C23×C197 | C22⋊C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C197 ◁ C2×C42×C197 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #333×C197 | C2 | semidirect |
| 5. #332×C197 | C2 | semidirect |
| 75. C197 | #1542 | direct (N × H) |
| 76. #1542 | C197 | direct (N × H) |
| 80. #333 | C2×C197 | semidirect |
| 81. #332 | C2×C197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #533×C197 | 2 |
| #431×C197 | 2 |
| C2×C4⋊C8×C197 | 2 |
| #333×C197 | 2 |
| #332×C197 | 2 |
| #1542 | 197 |