Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
200 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 200 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×C191 | #95 |
| commutator | C23 | C42×C191 |
| Frattini, cosocle | C23×C4 | C22×C191 |
| prime radical | C24×C191 | C2×C4 |
| LCS | G ▷ C23 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C191 ◁ C23×C4×C191 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. C2×M16×C191 | C4 | semidirect |
| 12. C22⋊C8×C191 | C4 | semidirect |
| 76. C191 | #1305 | direct (N × H) |
| 77. #1305 | C191 | direct (N × H) |
| 83. C2×M16 | C4×C191 | semidirect |
| 89. C22⋊C8 | C4×C191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #407×C191 | 2 |
| #380×C191 | 2 |
| #1305 | 191 |