Finite Group DatabasebetaFinite Group DatabasebetaOrder 24704.
266 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 68 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 | #120 |
| commutator, Frattini, cosocle | C22×C4 | C23×C193 |
| prime radical | C22×D4×C193 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C193 ◁ C22×C4×C193 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #544×C193 | C2 | semidirect |
| 4. #328×C193 | C2 | semidirect |
| 5. #324×C193 | C2 | semidirect |
| 63. C2×C4×C193 | SD16 | semidirect |
| 90. C193 | #1599 | direct (N × H) |
| 91. #1599 | C193 | direct (N × H) |
| 92. #544 | C2×C193 | semidirect |
| 95. #328 | C2×C193 | semidirect |
| 96. #324 | C2×C193 | semidirect |
| 154. C2×C4 | SD16×C193 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #544×C193 | 2 |
| #450×C193 | 2 |
| #394×C193 | 2 |
| #328×C193 | 2 |
| #324×C193 | 2 |
| #1599 | 193 |