Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
312 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 113 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 | C2×#41×C23 | C2 |
| hypercenter | C2×#41 | D23 |
| hypocenter | C23 | #550 |
| LCS | G ▷ C22×C23 ▷ C23 | |
| UCS | C1 ◁ C22 ◁ C2×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#41×C23 | C2 | semidirect |
| 2. C2×#67292 | C2 | semidirect |
| 3. Q8×Dic23 | C2 | semidirect |
| 4. #10625111 | C2 | semidirect |
| 5. #10625109 | C2 | semidirect |
| 6. #10625101 | C2 | semidirect |
| 7. C4×C22⋊D23 | C2 | semidirect |
| 24. Q8×C23 | D4 | semidirect |
| 47. Dic23 | #41 | semidirect |
| 55. C2×#41 | D23 | semidirect |
| 61. C23 | #550 | semidirect |
| 78. Q8 | C22⋊D23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#41×C23 | 2 |
| C2×#67292 | 2 |
| Q8×Dic23 | 2 |
| #10625111 | 2 |
| #10625109 | 2 |
| #10625101 | 2 |
| C4×C22⋊D23 | 2 |
| #550 | 23 |