Finite Group DatabasebetaFinite Group DatabasebetaOrder 24704.
234 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 64 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 | #99 |
| commutator | C23 | C42×C193 |
| Frattini, cosocle | C22×D4 | C22×C193 |
| prime radical | C22×D4×C193 | C22 |
| LCS | G ▷ C23 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C193 ◁ C23×C193 ◁ C22×D4×C193 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. C23×C4×C193 | C4 | semidirect |
| 9. C2×C22⋊C4×C193 | C4 | semidirect |
| 11. #100×C193 | C4 | semidirect |
| 13. #99×C193 | C4 | semidirect |
| 102. C193 | #1390 | direct (N × H) |
| 103. #1390 | C193 | direct (N × H) |
| 108. C23×C4 | C4×C193 | semidirect |
| 112. C2×C22⋊C4 | C4×C193 | semidirect |
| 114. #100 | C4×C193 | semidirect |
| 116. #99 | C4×C193 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#100×C193 | 2 |
| C2×#99×C193 | 2 |
| #386×C193 | 2 |
| #1390 | 193 |