Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
248 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22×C22⋊D23 |
| commutator, cosocle | C4×C23 | C24 |
| Frattini | C4 | C23×D23 |
| Fitting | C23×2−1+4 | C2 |
| socle | C2×C23 | C22×D4 |
| hypercenter | 2−1+4 | D23 |
| hypocenter | C23 | #578 |
| LCS | G ▷ C4×C23 ▷ C2×C23 ▷ C23 | |
| UCS | C1 ◁ C2 ◁ #41 ◁ 2−1+4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×2−1+4 | C2 | semidirect |
| 2. #10625161 | C2 | semidirect |
| 3. #10625122 | C2 | semidirect |
| 4. #10625121 | C2 | semidirect |
| 5. #10625119 | C2 | semidirect |
| 6. C2×#67275 | C2 | semidirect |
| 7. #10625113 | C2 | semidirect |
| 54. 2−1+4 | D23 | semidirect |
| 60. C23 | #578 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×2−1+4 | 2 |
| #10625161 | 2 |
| #10625122 | 2 |
| #10625121 | 2 |
| #10625119 | 2 |
| C2×#67275 | 2 |
| #10625113 | 2 |
| #578 | 23 |