Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
564 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 216 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 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C197 |
| socle | C22×C197 | C22×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ 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 |
|---|---|---|
| 1. C2×#135×C197 | C2 | semidirect |
| 2. #532×C197 | C2 | semidirect |
| 3. #497×C197 | C2 | semidirect |
| 4. #496×C197 | C2 | semidirect |
| 5. C2×#97×C197 | C2 | semidirect |
| 30. C2×C8×C197 | D4 | semidirect |
| 63. C197 | #3150 | direct (N × H) |
| 64. #3150 | C197 | direct (N × H) |
| 65. C2×#135 | C2×C197 | semidirect |
| 66. #532 | C2×C197 | semidirect |
| 67. #497 | C2×C197 | semidirect |
| 68. #496 | C2×C197 | semidirect |
| 69. C2×#97 | C2×C197 | semidirect |
| 94. C2×C8 | D4×C197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#135×C197 | 2 |
| #532×C197 | 2 |
| #497×C197 | 2 |
| #496×C197 | 2 |
| C2×#97×C197 | 2 |
| #3150 | 197 |