Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
592 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 232 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C197 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C197 |
| prime radical | C22×D8×C197 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C197 ◁ C2×C42×C197 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×Q16×C197 | C2 | semidirect |
| 2. C22×SD16×C197 | C2 | semidirect |
| 4. C2×#124×C197 | C2 | semidirect |
| 5. #495×C197 | C2 | direct (N × H) |
| 6. C2×C4×C8×C197 | C2 | semidirect |
| 10. C2×Q16×C197 | C22 | semidirect |
| 12. C2×SD16×C197 | C22 | semidirect |
| 18. #124×C197 | C22 | semidirect |
| 21. C4×C8×C197 | C22 | semidirect |
| 76. C2×C197 | #495 | direct (N × H) |
| 79. C197 | C2×#495 | direct (N × H) |
| 80. C2×#495 | C197 | direct (N × H) |
| 81. C22×Q16 | C2×C197 | semidirect |
| 82. C22×SD16 | C2×C197 | semidirect |
| 84. C2×#124 | C2×C197 | semidirect |
| 85. #495 | C2×C197 | direct (N × H) |
| 86. C2×C4×C8 | C2×C197 | semidirect |
| 90. C2×Q16 | C22×C197 | semidirect |
| 92. C2×SD16 | C22×C197 | semidirect |
| 98. #124 | C22×C197 | semidirect |
| 101. C4×C8 | C22×C197 | semidirect |
| 156. C2 | #495×C197 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q16×C197 | 2 |
| C22×SD16×C197 | 2 |
| C22×D8×C197 | 2 |
| C2×#124×C197 | 2 |
| #495×C197 | 2 |
| C2×C4×C8×C197 | 2 |
| C2×#495 | 197 |