Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
752 conjugacy classes of subgroups; only the 325 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 325 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C22×D97 |
| commutator | C2×C97 | C43 |
| Fitting | C2×#95×C97 | C2 |
| socle, prime radical, cosocle | C24×C97 | C23 |
| hypercenter | C2×#95 | D97 |
| hypocenter | C97 | C4×#95 |
| LCS | G ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C24 ◁ C2×#95 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 7. C2×C4×Dic97 | C4 | semidirect |
| 8. #15690717 | C4 | semidirect |
| 10. #95×C97 | C4 | semidirect |
| 37. C2×C4×C97 | C42 | semidirect |
| 43. C2×Dic97 | C42 | semidirect |
| 60. Dic97 | #95 | direct (N × H) |
| 69. C97 | C4×#95 | semidirect |
| 79. #95 | Dic97 | direct (N × H) |
| 114. C2×C4 | C4×Dic97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×Dic97 | 2 |
| C2×#15690717 | 2 |
| C2×#95×C97 | 2 |
| C4×#95 | 97 |