Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D19 |
| commutator, socle, cosocle | C23×C19 | C24 |
| Fitting | C2×C4×Q8×C19 | C2 |
| prime radical | C22×D76 | C22 |
| hypercenter | C2×C4×Q8 | D19 |
| hypocenter | C19 | #2632 |
| LCS | G ▷ C23×C19 ▷ C19 | |
| UCS | C1 ◁ C23 ◁ C2×C4×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11926479 | C2 | semidirect |
| 3. #11926464 | C2 | semidirect |
| 5. #11926455 | C2 | semidirect |
| 6. #11926435 | C2 | semidirect |
| 7. #11926412 | C2 | semidirect |
| 8. C2×C4×Q8×C19 | C2 | semidirect |
| 91. C2×C4×Q8 | D19 | semidirect |
| 121. C19 | #2632 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597321 | 2 |
| #11926479 | 2 |
| #11926464 | 2 |
| #11926461 | 2 |
| #11926455 | 2 |
| #11926435 | 2 |
| #11926412 | 2 |
| C2×C4×Q8×C19 | 2 |
| #2632 | 19 |