Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
160 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C97 | C2×D4 |
| commutator | C4 | C22×C8×C97 |
| Frattini, cosocle | C42 | C23×C97 |
| socle, prime radical | C22×C97 | C4×D4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C97 ◁ C4×C8×C97 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 17. Q16×C97 | C8 | semidirect |
| 49. #1579 | C97 | direct (N × H) |
| 50. C97 | #1579 | direct (N × H) |
| 67. Q16 | C8×C97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×Q8×C97 | 2 |
| C4×Q16×C97 | 2 |
| #334×C97 | 2 |
| Q8⋊C8×C97 | 2 |
| #322×C97 | 2 |
| #1579 | 97 |