Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
228 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 76 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×C197 | #120 |
| commutator, Frattini, cosocle | C42 | C23×C197 |
| prime radical | C2×D4×C197 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C197 ◁ C42×C197 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #487×C197 | C2 | semidirect |
| 3. #477×C197 | C2 | semidirect |
| 5. #332×C197 | C2 | semidirect |
| 6. Q8⋊C8×C197 | C2 | semidirect |
| 90. C197 | #1637 | direct (N × H) |
| 91. #1637 | C197 | direct (N × H) |
| 93. #487 | C2×C197 | semidirect |
| 94. #477 | C2×C197 | semidirect |
| 96. #332 | C2×C197 | semidirect |
| 97. Q8⋊C8 | C2×C197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Q8×C197 | 2 |
| #487×C197 | 2 |
| #477×C197 | 2 |
| #476×C197 | 2 |
| #332×C197 | 2 |
| Q8⋊C8×C197 | 2 |
| D4⋊C8×C197 | 2 |
| #1637 | 197 |