Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
1202 conjugacy classes of subgroups; only the 800 normal subgroups are shown.
This group has 1202 conjugacy classes of subgroups — too many to draw. Only its 800 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 | C24 |
| commutator, Frattini, cosocle | C22 | C25×C97 |
| socle | C22×C97 | C25 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C97 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. Q82×C97 | C2 | semidirect |
| 2. #555×C97 | C2 | semidirect |
| 3. #550×C97 | C2 | semidirect |
| 4. #532×C97 | C2 | semidirect |
| 5. C4×#41×C97 | C2 | semidirect |
| 34. Q8×C97 | #41 | semidirect |
| 53. #3483 | C97 | direct (N × H) |
| 54. C97 | #3483 | direct (N × H) |
| 55. Q82 | C2×C97 | semidirect |
| 56. #555 | C2×C97 | semidirect |
| 57. #550 | C2×C97 | semidirect |
| 58. #532 | C2×C97 | semidirect |
| 59. C4×#41 | C2×C97 | semidirect |
| 88. Q8 | #41×C97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q82×C97 | 2 |
| #555×C97 | 2 |
| #550×C97 | 2 |
| #532×C97 | 2 |
| C4×#41×C97 | 2 |
| #3483 | 97 |