Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
264 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 124 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×C199 | C2×D4 |
| commutator | C4 | C22×C8×C199 |
| Frattini, cosocle | C42 | C23×C199 |
| socle | C22×C199 | C2×C22⋊C4 |
| prime radical | C2×#41×C199 | C4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C199 ◁ C2×C42×C199 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #431×C199 | C2 | semidirect |
| 3. C2×C4⋊C8×C199 | C2 | semidirect |
| 4. Q8⋊C8×C199 | C2 | semidirect |
| 5. D4⋊C8×C199 | C2 | semidirect |
| 24. #41×C199 | C8 | semidirect |
| 54. Q8×C199 | C2×C8 | semidirect |
| 57. D4×C199 | C2×C8 | semidirect |
| 101. C199 | #1477 | direct (N × H) |
| 102. #1477 | C199 | direct (N × H) |
| 104. #431 | C2×C199 | semidirect |
| 105. C2×C4⋊C8 | C2×C199 | semidirect |
| 106. Q8⋊C8 | C2×C199 | semidirect |
| 107. D4⋊C8 | C2×C199 | semidirect |
| 126. #41 | C8×C199 | semidirect |
| 156. Q8 | C2×C8×C199 | semidirect |
| 159. D4 | C2×C8×C199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#41×C199 | 2 |
| #431×C199 | 2 |
| C2×C4⋊C8×C199 | 2 |
| Q8⋊C8×C199 | 2 |
| D4⋊C8×C199 | 2 |
| #1477 | 199 |