Finite Group DatabasebetaFinite Group DatabasebetaOrder 24704.
224 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 224 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×C8×C193 | D4 |
| commutator | C4 | C22×C8×C193 |
| Frattini, cosocle | C2×C8 | C23×C193 |
| socle | C22×C193 | C22⋊C8 |
| prime radical | C2×#41×C193 | C4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C193 ◁ C22×C8×C193 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×M32×C193 | C2 | semidirect |
| 3. C22×C16×C193 | C2 | semidirect |
| 4. #350×C193 | C2 | direct (N × H) |
| 15. M32×C193 | C22 | semidirect |
| 19. C2×C16×C193 | C22 | semidirect |
| 80. C2×C193 | #350 | direct (N × H) |
| 82. C193 | C2×#350 | direct (N × H) |
| 83. C2×#350 | C193 | direct (N × H) |
| 85. C2×M32 | C2×C193 | semidirect |
| 86. C22×C16 | C2×C193 | semidirect |
| 87. #350 | C2×C193 | direct (N × H) |
| 98. M32 | C22×C193 | semidirect |
| 102. C2×C16 | C22×C193 | semidirect |
| 163. C2 | #350×C193 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#131×C193 | 2 |
| C2×M32×C193 | 2 |
| C22×C16×C193 | 2 |
| #350×C193 | 2 |
| C2×#350 | 193 |