Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
148 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C97 | #466 |
| commutator, Frattini, cosocle | C2×C8 | C23×C97 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C97 ◁ C2×C4×C97 ◁ #131×C97 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×D16×C97 | C2 | semidirect |
| 2. #504×C97 | C2 | semidirect |
| 3. #472×C97 | C2 | semidirect |
| 4. #368×C97 | C2 | semidirect |
| 5. #361×C97 | C2 | semidirect |
| 54. #2221 | C97 | direct (N × H) |
| 55. C97 | #2221 | direct (N × H) |
| 56. C2×D16 | C2×C97 | semidirect |
| 57. #504 | C2×C97 | semidirect |
| 58. #472 | C2×C97 | semidirect |
| 59. #368 | C2×C97 | semidirect |
| 60. #361 | C2×C97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D16×C97 | 2 |
| #504×C97 | 2 |
| #472×C97 | 2 |
| #368×C97 | 2 |
| #361×C97 | 2 |
| #2221 | 97 |