Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
1224 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 1224 conjugacy classes of subgroups — too many to draw. Only its 237 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D109 |
| commutator, socle, cosocle | C23×C109 | C24 |
| Fitting | C24×C4×C109 | C2 |
| hypercenter | C24×C4 | D109 |
| hypocenter | C109 | #2847 |
| LCS | G ▷ C23×C109 ▷ C109 | |
| UCS | C1 ◁ C23 ◁ C24×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#16812673 | C2 | semidirect |
| 2. C2×#16812668 | C2 | semidirect |
| 3. #20294905 | C2 | semidirect |
| 4. #20294886 | C2 | semidirect |
| 5. C24×C4×C109 | C2 | semidirect |
| 6. C22×D436 | C22 | semidirect |
| 10. C2×C4⋊Dic109 | C22 | semidirect |
| 12. C2×#13182006 | C22 | semidirect |
| 13. #16812606 | C22 | semidirect |
| 29. C24×C109 | D4 | semidirect |
| 35. C22×C4×C109 | D4 | semidirect |
| 65. C22×C109 | #121 | semidirect |
| 73. C4×C109 | #120 | semidirect |
| 81. C109 | #2847 | semidirect |
| 82. C24×C4 | D109 | semidirect |
| 102. C24 | D436 | semidirect |
| 113. C22×C4 | C22⋊D109 | semidirect |
| 149. C22 | #16812673 | semidirect |
| 155. C4 | #16812668 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812673 | 2 |
| C2×#16812668 | 2 |
| #20294905 | 2 |
| #20294886 | 2 |
| C24×C4×C109 | 2 |
| #2847 | 109 |