Finite Group DatabasebetaFinite Group DatabasebetaOrder 14272.
310 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 310 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, Frattini | C22 | C23×D223 |
| commutator, socle, cosocle | C22×C223 | C24 |
| Fitting | #124×C223 | C2 |
| hypercenter | #124 | D223 |
| hypocenter | C223 | #532 |
| LCS | G ▷ C22×C223 ▷ C223 | |
| UCS | C1 ◁ C22 ◁ #124 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#16813171 | C2 | semidirect |
| 2. C2×#16813169 | C2 | semidirect |
| 3. #20297302 | C2 | semidirect |
| 4. #20297300 | C2 | semidirect |
| 5. #20297292 | C2 | semidirect |
| 6. #20297277 | C2 | semidirect |
| 7. (C22⋊D223)⋊C4 | C2 | semidirect |
| 8. C42×D223 | C2 | semidirect |
| 9. #124×C223 | C2 | semidirect |
| 42. C4×D223 | D4 | semidirect |
| 61. Dic223 | #41 | semidirect |
| 67. C223 | #532 | semidirect |
| 74. #124 | D223 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813171 | 2 |
| C2×#16813169 | 2 |
| #20297302 | 2 |
| #20297300 | 2 |
| #20297292 | 2 |
| #20297277 | 2 |
| (C22⋊D223)⋊C4 | 2 |
| C42×D223 | 2 |
| #124×C223 | 2 |
| #532 | 223 |