Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
186 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C97 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C23×C97 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C97 ◁ C42×C97 ◁ C4×C8×C97 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×D16×C97 | C2 | semidirect |
| 2. #493×C97 | C2 | semidirect |
| 3. C4×D8×C97 | C2 | semidirect |
| 4. C4⋊C16×C97 | C2 | semidirect |
| 5. #357×C97 | C2 | semidirect |
| 25. D8×C97 | D4 | semidirect |
| 57. C4×C97 | D16 | semidirect |
| 65. #2206 | C97 | direct (N × H) |
| 66. C97 | #2206 | direct (N × H) |
| 67. C2×D16 | C2×C97 | semidirect |
| 68. #493 | C2×C97 | semidirect |
| 69. C4×D8 | C2×C97 | semidirect |
| 70. C4⋊C16 | C2×C97 | semidirect |
| 71. #357 | C2×C97 | semidirect |
| 91. D8 | D4×C97 | semidirect |
| 123. C4 | D16×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 |
| #493×C97 | 2 |
| C4×D8×C97 | 2 |
| C4⋊C16×C97 | 2 |
| #357×C97 | 2 |
| #2206 | 97 |