Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
170 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 60 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×C197 | #459 |
| commutator, Frattini, cosocle | C2×C8 | C23×C197 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C197 ◁ C2×C4×C197 ◁ C4×C8×C197 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #509×C197 | C2 | semidirect |
| 2. #493×C197 | C2 | semidirect |
| 3. #443×C197 | C2 | semidirect |
| 4. #364×C197 | C2 | semidirect |
| 5. #361×C197 | C2 | semidirect |
| 20. Q16×C197 | D4 | semidirect |
| 26. D8×C197 | D4 | semidirect |
| 61. C197 | #2213 | direct (N × H) |
| 62. #2213 | C197 | direct (N × H) |
| 63. #509 | C2×C197 | semidirect |
| 64. #493 | C2×C197 | semidirect |
| 65. #443 | C2×C197 | semidirect |
| 66. #364 | C2×C197 | semidirect |
| 67. #361 | C2×C197 | semidirect |
| 82. Q16 | D4×C197 | semidirect |
| 88. D8 | D4×C197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #509×C197 | 2 |
| #493×C197 | 2 |
| #443×C197 | 2 |
| #364×C197 | 2 |
| #361×C197 | 2 |
| #2213 | 197 |