Finite Group DatabasebetaFinite Group DatabasebetaOrder 24704.
440 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 104 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×C193 | C2×C22⋊C4 |
| commutator | C23 | C22×C4×C193 |
| Frattini, cosocle | C22×C4 | C23×C193 |
| prime radical | C25×C193 | C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C193 ◁ C23×C4×C193 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #407×C193 | C2 | semidirect |
| 3. #323×C193 | C2 | semidirect |
| 13. C22⋊C8×C193 | C22 | semidirect |
| 50. C23×C193 | M16 | semidirect |
| 91. C193 | #1462 | direct (N × H) |
| 92. #1462 | C193 | direct (N × H) |
| 94. #407 | C2×C193 | semidirect |
| 95. #323 | C2×C193 | semidirect |
| 105. C22⋊C8 | C22×C193 | semidirect |
| 142. C23 | M16×C193 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊C4×C193 | 2 |
| #407×C193 | 2 |
| #323×C193 | 2 |
| #1462 | 193 |