Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
280 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 115 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 | C23×D23 |
| commutator, socle, cosocle | C22×C23 | C24 |
| Fitting | C23×C22⋊Q8 | C2 |
| prime radical | C2×C22⋊D23 | C22 |
| hypercenter | C22⋊Q8 | D23 |
| hypocenter | C23 | D4×Q8 |
| LCS | G ▷ C22×C23 ▷ C23 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×Q8×D23 | C2 | semidirect |
| 2. C22×Dic46 | C2 | semidirect |
| 3. C23×C22⋊Q8 | C2 | semidirect |
| 4. #10625115 | C2 | semidirect |
| 6. #10625068 | C2 | semidirect |
| 7. #10625067 | C2 | semidirect |
| 8. #10625059 | C2 | semidirect |
| 9. #10625058 | C2 | semidirect |
| 11. #10625049 | C2 | semidirect |
| 45. C22⋊D23 | Q8 | semidirect |
| 57. Dic46 | D4 | semidirect |
| 60. C22×C23 | C2×Q8 | semidirect |
| 64. C2×D23 | C2×Q8 | semidirect |
| 73. Dic23 | C2×Q8 | semidirect |
| 87. C22⋊Q8 | D23 | semidirect |
| 91. C23 | D4×Q8 | semidirect |
| 143. C22 | Q8×D23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×D23 | 2 |
| C22×Dic46 | 2 |
| C23×C22⋊Q8 | 2 |
| #10625115 | 2 |
| C4×C22⋊D23 | 2 |
| #10625068 | 2 |
| #10625067 | 2 |
| #10625059 | 2 |
| #10625058 | 2 |
| (C22⋊D23)⋊C4 | 2 |
| #10625049 | 2 |
| D4×Q8 | 23 |