Finite Group DatabasebetaFinite Group DatabasebetaOrder 24256.
310 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 119 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D379 |
| commutator, socle, cosocle | C22×C379 | C24 |
| Frattini | C22 | C23×D379 |
| Fitting | C2×C42×C379 | C2 |
| hypercenter | C2×C42 | D379 |
| hypocenter | C379 | #532 |
| LCS | G ▷ C22×C379 ▷ C379 | |
| UCS | C1 ◁ C2×C4 ◁ C2×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#20258606 | C2 | semidirect |
| 2. #27131331 | C2 | semidirect |
| 3. #27131328 | C2 | semidirect |
| 4. #27131319 | C2 | semidirect |
| 5. #27131305 | C2 | semidirect |
| 6. C4×D1516 | C2 | semidirect |
| 7. C2×C42×C379 | C2 | semidirect |
| 30. C2×C4×C379 | D4 | semidirect |
| 43. C4×C379 | #41 | semidirect |
| 49. C379 | #532 | semidirect |
| 57. C2×C42 | D379 | semidirect |
| 80. C2×C4 | D1516 | semidirect |
| 94. C4 | #20258606 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20258606 | 2 |
| #27131331 | 2 |
| #27131328 | 2 |
| #27131319 | 2 |
| #27131305 | 2 |
| C4×D1516 | 2 |
| C2×C42×C379 | 2 |
| #532 | 379 |