Finite Group DatabasebetaFinite Group DatabasebetaOrder 24704.
476 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 200 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C193 | C23 |
| commutator | C23 | C22×C4×C193 |
| Frattini, cosocle | C24 | C23×C193 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C193 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 9. #95×C193 | C4 | semidirect |
| 75. C193 | #1443 | direct (N × H) |
| 76. #1443 | C193 | direct (N × H) |
| 85. #95 | C4×C193 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#95×C193 | 2 |
| #1443 | 193 |