Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
1492 conjugacy classes of subgroups; only the 553 normal subgroups are shown.
This group has 1492 conjugacy classes of subgroups — too many to draw. Only its 553 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D19 |
| commutator, socle, cosocle | C22×C19 | C25 |
| Fitting | C2×C4×Q8×C19 | C2 |
| hypercenter | C2×C4×Q8 | D19 |
| hypocenter | C19 | #3497 |
| LCS | G ▷ C22×C19 ▷ C19 | |
| UCS | C1 ◁ C22 ◁ C2×C4×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10597433 | C2 | semidirect |
| 2. #11927216 | C2 | semidirect |
| 3. Q8×D76 | C2 | semidirect |
| 4. #11927206 | C2 | semidirect |
| 5. #11927125 | C2 | semidirect |
| 6. #11927094 | C2 | semidirect |
| 7. C2×C4×Q8×C19 | C2 | semidirect |
| 26. C2×Q8×C19 | D4 | semidirect |
| 75. C4×C19 | 2−1+4 | semidirect |
| 83. C2×C4×Q8 | D19 | semidirect |
| 107. C19 | #3497 | semidirect |
| 112. C2×Q8 | D76 | semidirect |
| 157. C4 | #10597433 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597433 | 2 |
| #11927216 | 2 |
| Q8×D76 | 2 |
| #11927206 | 2 |
| #11927125 | 2 |
| #11927094 | 2 |
| C2×C4×Q8×C19 | 2 |
| #3497 | 19 |