Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
314 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 314 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×C199 | #120 |
| commutator, Frattini, cosocle | C42 | C23×C199 |
| prime radical | D42×C199 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C199 ◁ C42×C199 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #492×C199 | C2 | semidirect |
| 3. #476×C199 | C2 | semidirect |
| 4. #331×C199 | C2 | semidirect |
| 5. D4⋊C8×C199 | C2 | semidirect |
| 8. C4⋊Q8×C199 | C22 | semidirect |
| 14. C4⋊C8×C199 | C22 | semidirect |
| 16. C4×C8×C199 | C22 | semidirect |
| 44. D4×C199 | SD16 | semidirect |
| 69. C199 | #1629 | direct (N × H) |
| 70. #1629 | C199 | direct (N × H) |
| 72. #492 | C2×C199 | semidirect |
| 73. #476 | C2×C199 | semidirect |
| 74. #331 | C2×C199 | semidirect |
| 75. D4⋊C8 | C2×C199 | semidirect |
| 78. C4⋊Q8 | C22×C199 | semidirect |
| 84. C4⋊C8 | C22×C199 | semidirect |
| 86. C4×C8 | C22×C199 | semidirect |
| 114. D4 | SD16×C199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D42×C199 | 2 |
| #492×C199 | 2 |
| #476×C199 | 2 |
| #331×C199 | 2 |
| D4⋊C8×C199 | 2 |
| #1629 | 199 |