Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
192 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 192 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 | C22×C97 | C4×D4 |
| prime radical | C2×D8×C97 | C4 |
| 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 |
|---|---|---|
| 2. C8×D4×C97 | C2 | semidirect |
| 3. #334×C97 | C2 | semidirect |
| 4. D4⋊C8×C97 | C2 | semidirect |
| 5. #322×C97 | C2 | semidirect |
| 18. D8×C97 | C8 | semidirect |
| 30. D4×C97 | C2×C8 | semidirect |
| 41. C8×C97 | C2×C8 | semidirect |
| 55. #1580 | C97 | direct (N × H) |
| 56. C97 | #1580 | direct (N × H) |
| 58. C8×D4 | C2×C97 | semidirect |
| 59. #334 | C2×C97 | semidirect |
| 60. D4⋊C8 | C2×C97 | semidirect |
| 61. #322 | C2×C97 | semidirect |
| 74. D8 | C8×C97 | semidirect |
| 86. D4 | C2×C8×C97 | semidirect |
| 97. C8 | C2×C8×C97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D8×C97 | 2 |
| C8×D4×C97 | 2 |
| #334×C97 | 2 |
| D4⋊C8×C97 | 2 |
| #322×C97 | 2 |
| #1580 | 97 |