Finite Group DatabasebetaFinite Group DatabasebetaOrder 24704.
264 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 120 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×C193 | C22⋊C4 |
| commutator | C22 | C22×C8×C193 |
| Frattini, cosocle | C22×C4 | C23×C193 |
| socle | C22×C193 | C2×C22⋊C4 |
| prime radical | C24×C193 | C2×C4 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C193 ◁ C2×C42×C193 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #431×C193 | C2 | semidirect |
| 3. #324×C193 | C2 | semidirect |
| 21. C22×C4×C193 | C8 | semidirect |
| 84. C193 | #1458 | direct (N × H) |
| 85. #1458 | C193 | direct (N × H) |
| 87. #431 | C2×C193 | semidirect |
| 88. #324 | C2×C193 | semidirect |
| 106. C22×C4 | C8×C193 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#117×C193 | 2 |
| #431×C193 | 2 |
| #324×C193 | 2 |
| #323×C193 | 2 |
| #1458 | 193 |