Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
426 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D23 |
| commutator, cosocle | C22×C23 | C24 |
| Frattini | C22 | C23×D23 |
| Fitting | C2×C22⋊C4×C23 | C2 |
| socle | C23×C23 | C23 |
| hypercenter | C2×C22⋊C4 | D23 |
| hypocenter | C23 | C2×#121 |
| LCS | G ▷ C22×C23 ▷ C23 | |
| UCS | C1 ◁ C23 ◁ C2×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C22⋊D23 | C2 | semidirect |
| 2. C22×C22⋊D23 | C2 | semidirect |
| 3. C22×D92 | C2 | semidirect |
| 4. C22×C4×D23 | C2 | semidirect |
| 5. C2×C22⋊C4×C23 | C2 | semidirect |
| 6. C2×(C2×D23)⋊C4 | C2 | semidirect |
| 7. C2×Dic23⋊C4 | C2 | semidirect |
| 8. #10625055 | C2 | direct (N × H) |
| 16. C2×C22⋊D23 | C22 | semidirect |
| 17. C2×C22⋊D23 | C22 | semidirect |
| 21. C2×D92 | C22 | semidirect |
| 23. C2×C4×D23 | C22 | semidirect |
| 24. C22⋊C4×C23 | C22 | semidirect |
| 25. (C2×D23)⋊C4 | C22 | semidirect |
| 26. Dic23⋊C4 | C22 | semidirect |
| 37. C22×D23 | D4 | semidirect |
| 47. C2×Dic23 | D4 | semidirect |
| 67. C2×D23 | C2×D4 | semidirect |
| 71. Dic23 | C2×D4 | semidirect |
| 74. C2×C23 | #121 | semidirect |
| 87. C2×C22⋊C4 | D23 | semidirect |
| 88. C23 | C2×#121 | semidirect |
| 106. C22⋊C4 | C2×D23 | semidirect |
| 155. C2 | #10625055 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊D23 | 2 |
| C22×D92 | 2 |
| C22×C4×D23 | 2 |
| C2×C22⋊C4×C23 | 2 |
| C2×(C2×D23)⋊C4 | 2 |
| C2×Dic23⋊C4 | 2 |
| #10625055 | 2 |
| C2×#121 | 23 |