Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
382 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 92 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 | C22×C4 | C23×C199 |
| prime radical | C2×AGL(1,ℤ/8)×C199 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C199 ◁ C22×C4×C199 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #536×C199 | C2 | semidirect |
| 3. C2×#124×C199 | C2 | semidirect |
| 4. C2×#104×C199 | C2 | semidirect |
| 5. #418×C199 | C2 | semidirect |
| 6. C2×#101×C199 | C2 | semidirect |
| 7. #339×C199 | C2 | semidirect |
| 130. C199 | #2003 | direct (N × H) |
| 131. #2003 | C199 | direct (N × H) |
| 133. #536 | C2×C199 | semidirect |
| 134. C2×#124 | C2×C199 | semidirect |
| 135. C2×#104 | C2×C199 | semidirect |
| 136. #418 | C2×C199 | semidirect |
| 137. C2×#101 | C2×C199 | semidirect |
| 138. #339 | C2×C199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×AGL(1,ℤ/8)×C199 | 2 |
| #536×C199 | 2 |
| C2×#124×C199 | 2 |
| C2×#104×C199 | 2 |
| #418×C199 | 2 |
| C2×#101×C199 | 2 |
| #339×C199 | 2 |
| #2003 | 199 |